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Class 11 Physics - Rotation
Linear Momentum and Conservation Laws
Master momentum, impulse, conservation laws, recoil, rocket motion, explosions, numericals and PYQs.
CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
01
Linear Momentum
Linear momentum is the quantity of motion of a body. It is a vector and its direction is the same as velocity direction.
p = mv
- Vector nature: direction along velocity.
- SI unit: kg m/s.
- Dimensions: ML T-1.
- For same velocity, heavier body has more momentum.
02
Impulse
Impulse is the effect of force acting for a time interval. It equals change in momentum.
J = FΔtJ = ∫FdtJ = Δp
Area under the force-time graph gives impulse. Bat-ball collision, airbags and seat belts are impulse applications.
03
Conservation of Momentum
If net external impulse is zero, total momentum remains constant. Internal forces cancel due to Newton's third law.
m1u1 + m2u2 = m1v1 + m2v2
Use signed velocities. The system must be isolated or external impulse must be negligible.
04
Recoil
Gun recoil, rifle recoil and cannon recoil happen because total initial momentum is zero and final momenta must add to zero.
MV = mv
Gun momentum equals bullet momentum in opposite direction. The bullet gets much more kinetic energy because its mass is smaller.
05
Rocket Motion
Rocket motion is a variable mass system. Hot gases leave backward with exhaust velocity, producing forward thrust.
v = u ln(M0/M)Thrust = u(dm/dt)
- u is exhaust speed relative to rocket.
- M0 is initial mass; M is current mass.
- Multi-stage rockets improve mass ratio.
06
Explosions
Explosions involve internal forces. Momentum is conserved if external impulse is negligible, but kinetic energy may increase due to internal energy release.
- Explosion at rest: vector sum of final momenta is zero.
- Explosion in motion: final total momentum equals initial momentum.
- COM motion is not changed by internal explosion forces.
07
Applications
Real-world momentum and impulse applications with concept, diagram, formula and exam tip.
Gun recoil
Concept: Momentum conservation
Formula: MV=mv
Exam Tip: Recoil is opposite bullet direction.
Rocket launch
Concept: Backward exhaust creates forward thrust
Formula: v=u ln(M0/M)
Exam Tip: Mass ratio matters.
Jet propulsion
Concept: Air/exhaust momentum changes
Formula: Thrust = rate of momentum change
Exam Tip: Use relative exhaust velocity.
Balloon motion
Concept: Air rushes backward, balloon moves forward
Formula: Σp conserved
Exam Tip: Direction is opposite escaping air.
Firecracker explosion
Concept: Internal energy separates fragments
Formula: Σp after = Σp before
Exam Tip: Vector sum matters.
Spacecraft manoeuvres
Concept: Small gas jets change momentum
Formula: J=Δp
Exam Tip: Works in vacuum.
Airbag systems
Concept: Impulse spread over longer time
Formula: Favg=Δp/Δt
Exam Tip: Larger time reduces force.
Seat belt systems
Concept: Controlled stopping time
Formula: J=Δp
Exam Tip: Prevents sudden large force.
Cricket bat impact
Concept: Bat gives impulse to ball
Formula: J=m(v-u)
Exam Tip: Use signs for reversal.
Car collision
Concept: Momentum and impulse safety
Formula: Favg=Δp/Δt
Exam Tip: Crumple zones increase stopping time.
08
Important Graphs
Momentum and impulse graphs make formulas visual.
Momentum vs Velocity
Straight line through origin; slope equals mass.
Momentum vs Mass
For constant velocity, p is proportional to mass.
Force vs Time
Area under graph is impulse.
Impulse vs Time
Slope gives force when force varies smoothly.
Area Under F-t
Rectangle, triangle or trapezium area gives J.
Searching for a Physics Tutor? If Momentum, Recoil, Rocket Motion, Explosions or NEET/JEE numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com
09
High-Quality Numericals
Solved numerical bank for CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE and A-Level.
1. CBSE momentum: A 5 kg body moves at 4 m/s. Find momentum.
Question: A 5 kg body moves at 4 m/s. Find momentum.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: p=mv=20 kg m/s.
Final Answer: p=mv=20 kg m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: p=mv=20 kg m/s.
Final Answer: p=mv=20 kg m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
2. NEET impulse: A 50 N force acts for 0.2 s. Find impulse.
Question: A 50 N force acts for 0.2 s. Find impulse.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: J=FΔt=10 N s.
Final Answer: J=FΔt=10 N s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: J=FΔt=10 N s.
Final Answer: J=FΔt=10 N s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
3. JEE Main recoil: Bullet 0.01 kg at 500 m/s leaves 2.5 kg gun. Find recoil speed.
Question: Bullet 0.01 kg at 500 m/s leaves 2.5 kg gun. Find recoil speed.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: V=mv/M=2 m/s opposite bullet.
Final Answer: V=mv/M=2 m/s opposite bullet.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: V=mv/M=2 m/s opposite bullet.
Final Answer: V=mv/M=2 m/s opposite bullet.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
4. JEE Advanced rocket: Find rocket speed gain if u=2 km/s and M0/M=4.
Question: Find rocket speed gain if u=2 km/s and M0/M=4.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: Δv=2 ln4=2.77 km/s.
Final Answer: Δv=2 ln4=2.77 km/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: Δv=2 ln4=2.77 km/s.
Final Answer: Δv=2 ln4=2.77 km/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
5. IB explosion: Mass 4 kg at rest splits into 1 kg at 12 m/s and 3 kg. Find velocity of 3 kg.
Question: Mass 4 kg at rest splits into 1 kg at 12 m/s and 3 kg. Find velocity of 3 kg.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: 0=12+3v, v=-4 m/s.
Final Answer: 0=12+3v, v=-4 m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: 0=12+3v, v=-4 m/s.
Final Answer: 0=12+3v, v=-4 m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
6. IGCSE collision: 1 kg cart at 6 m/s sticks to 2 kg cart at rest. Find speed.
Question: 1 kg cart at 6 m/s sticks to 2 kg cart at rest. Find speed.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: v=6/3=2 m/s.
Final Answer: v=6/3=2 m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: v=6/3=2 m/s.
Final Answer: v=6/3=2 m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
7. A-Level force-time: F=10t from 0 to 3 s. Find impulse.
Question: F=10t from 0 to 3 s. Find impulse.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: J=∫10t dt=45 N s.
Final Answer: J=∫10t dt=45 N s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: J=∫10t dt=45 N s.
Final Answer: J=∫10t dt=45 N s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
8. Multi-body momentum: Masses 1,2,3 kg have velocities 2,0,-1 m/s. Total momentum?
Question: Masses 1,2,3 kg have velocities 2,0,-1 m/s. Total momentum?
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: P=2+0-3=-1 kg m/s.
Final Answer: P=2+0-3=-1 kg m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: P=2+0-3=-1 kg m/s.
Final Answer: P=2+0-3=-1 kg m/s.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
9. Airbag force: Momentum change 600 kg m/s in 0.2 s. Average force?
Question: Momentum change 600 kg m/s in 0.2 s. Average force?
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: F=3000 N.
Final Answer: F=3000 N.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: F=3000 N.
Final Answer: F=3000 N.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
10. Explosion in motion: A 6 kg shell moving 5 m/s explodes. Total momentum after?
Question: A 6 kg shell moving 5 m/s explodes. Total momentum after?
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: P=30 kg m/s in original direction.
Final Answer: P=30 kg m/s in original direction.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
Diagram: shown above.
Given: Identify masses, velocities, force and time from the question.
Formula: p=mv, J=FΔt=Δp, and for isolated systems Σpbefore=Σpafter.
Calculation: P=30 kg m/s in original direction.
Final Answer: P=30 kg m/s in original direction.
Exam Tip: Choose one positive direction first.
Common Mistake: Treating momentum as scalar and dropping signs.
10
NEET Question Bank
50 NEET-style MCQs. Authentic years are not invented.
1. NEET Exam-style Question: A 2 kg body moves at 5 m/s. Momentum is: A 5 B 7 C 10 D 20 kg m/s
Correct Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
2. NEET Exam-style Question: A force of 20 N acts for 0.5 s. Impulse is: A 5 B 10 C 20 D 40 N s
Correct Answer: B. J=FΔt=10 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
3. NEET Exam-style Question: Two bodies stick after collision. Conserved quantity for isolated system is: A KE B momentum C speed D force
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
4. NEET Exam-style Question: A gun recoils because of conservation of: A charge B momentum C power D energy only
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
5. NEET Exam-style Question: Rocket moves forward by ejecting gases backward due to: A inertia only B momentum conservation C gravity only D friction
Correct Answer: B.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
6. NEET Exam-style Question: A bomb at rest explodes into fragments. Total momentum just after explosion is: A zero B infinite C negative always D nonzero always
Correct Answer: A, if external impulse is negligible.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
7. NEET Exam-style Question: Momentum direction is same as: A acceleration B displacement always C velocity D force always
Correct Answer: C.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
8. NEET Exam-style Question: SI unit of impulse is: A J B W C N s D kg
Correct Answer: C. Also kg m/s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
9. NEET Exam-style Question: Airbags reduce average force by increasing: A mass B stopping time C momentum change D speed
Correct Answer: B.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
10. NEET Exam-style Question: Momentum conservation requires net external impulse to be: A zero B maximum C negative D infinite
Correct Answer: A.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
11. NEET Exam-style Question: A 2 kg body moves at 5 m/s. Momentum is: A 5 B 7 C 10 D 20 kg m/s
Correct Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
12. NEET Exam-style Question: A force of 20 N acts for 0.5 s. Impulse is: A 5 B 10 C 20 D 40 N s
Correct Answer: B. J=FΔt=10 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
13. NEET Exam-style Question: Two bodies stick after collision. Conserved quantity for isolated system is: A KE B momentum C speed D force
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
14. NEET Exam-style Question: A gun recoils because of conservation of: A charge B momentum C power D energy only
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
15. NEET Exam-style Question: Rocket moves forward by ejecting gases backward due to: A inertia only B momentum conservation C gravity only D friction
Correct Answer: B.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
16. NEET Exam-style Question: A bomb at rest explodes into fragments. Total momentum just after explosion is: A zero B infinite C negative always D nonzero always
Correct Answer: A, if external impulse is negligible.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
17. NEET Exam-style Question: Momentum direction is same as: A acceleration B displacement always C velocity D force always
Correct Answer: C.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
18. NEET Exam-style Question: SI unit of impulse is: A J B W C N s D kg
Correct Answer: C. Also kg m/s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
19. NEET Exam-style Question: Airbags reduce average force by increasing: A mass B stopping time C momentum change D speed
Correct Answer: B.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
20. NEET Exam-style Question: Momentum conservation requires net external impulse to be: A zero B maximum C negative D infinite
Correct Answer: A.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
21. NEET Exam-style Question: A 2 kg body moves at 5 m/s. Momentum is: A 5 B 7 C 10 D 20 kg m/s
Correct Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
22. NEET Exam-style Question: A force of 20 N acts for 0.5 s. Impulse is: A 5 B 10 C 20 D 40 N s
Correct Answer: B. J=FΔt=10 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
23. NEET Exam-style Question: Two bodies stick after collision. Conserved quantity for isolated system is: A KE B momentum C speed D force
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
24. NEET Exam-style Question: A gun recoils because of conservation of: A charge B momentum C power D energy only
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
25. NEET Exam-style Question: Rocket moves forward by ejecting gases backward due to: A inertia only B momentum conservation C gravity only D friction
Correct Answer: B.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
26. NEET Exam-style Question: A bomb at rest explodes into fragments. Total momentum just after explosion is: A zero B infinite C negative always D nonzero always
Correct Answer: A, if external impulse is negligible.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
27. NEET Exam-style Question: Momentum direction is same as: A acceleration B displacement always C velocity D force always
Correct Answer: C.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
28. NEET Exam-style Question: SI unit of impulse is: A J B W C N s D kg
Correct Answer: C. Also kg m/s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
29. NEET Exam-style Question: Airbags reduce average force by increasing: A mass B stopping time C momentum change D speed
Correct Answer: B.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
30. NEET Exam-style Question: Momentum conservation requires net external impulse to be: A zero B maximum C negative D infinite
Correct Answer: A.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
31. NEET Exam-style Question: A 2 kg body moves at 5 m/s. Momentum is: A 5 B 7 C 10 D 20 kg m/s
Correct Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
32. NEET Exam-style Question: A force of 20 N acts for 0.5 s. Impulse is: A 5 B 10 C 20 D 40 N s
Correct Answer: B. J=FΔt=10 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
33. NEET Exam-style Question: Two bodies stick after collision. Conserved quantity for isolated system is: A KE B momentum C speed D force
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
34. NEET Exam-style Question: A gun recoils because of conservation of: A charge B momentum C power D energy only
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
35. NEET Exam-style Question: Rocket moves forward by ejecting gases backward due to: A inertia only B momentum conservation C gravity only D friction
Correct Answer: B.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
36. NEET Exam-style Question: A bomb at rest explodes into fragments. Total momentum just after explosion is: A zero B infinite C negative always D nonzero always
Correct Answer: A, if external impulse is negligible.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
37. NEET Exam-style Question: Momentum direction is same as: A acceleration B displacement always C velocity D force always
Correct Answer: C.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
38. NEET Exam-style Question: SI unit of impulse is: A J B W C N s D kg
Correct Answer: C. Also kg m/s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
39. NEET Exam-style Question: Airbags reduce average force by increasing: A mass B stopping time C momentum change D speed
Correct Answer: B.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
40. NEET Exam-style Question: Momentum conservation requires net external impulse to be: A zero B maximum C negative D infinite
Correct Answer: A.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
41. NEET Exam-style Question: A 2 kg body moves at 5 m/s. Momentum is: A 5 B 7 C 10 D 20 kg m/s
Correct Answer: C. p=mv=10 kg m/s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests linear momentum. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
42. NEET Exam-style Question: A force of 20 N acts for 0.5 s. Impulse is: A 5 B 10 C 20 D 40 N s
Correct Answer: B. J=FΔt=10 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
43. NEET Exam-style Question: Two bodies stick after collision. Conserved quantity for isolated system is: A KE B momentum C speed D force
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
44. NEET Exam-style Question: A gun recoils because of conservation of: A charge B momentum C power D energy only
Correct Answer: B. Momentum.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
45. NEET Exam-style Question: Rocket moves forward by ejecting gases backward due to: A inertia only B momentum conservation C gravity only D friction
Correct Answer: B.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
46. NEET Exam-style Question: A bomb at rest explodes into fragments. Total momentum just after explosion is: A zero B infinite C negative always D nonzero always
Correct Answer: A, if external impulse is negligible.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
47. NEET Exam-style Question: Momentum direction is same as: A acceleration B displacement always C velocity D force always
Correct Answer: C.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector nature. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
48. NEET Exam-style Question: SI unit of impulse is: A J B W C N s D kg
Correct Answer: C. Also kg m/s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests unit. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
49. NEET Exam-style Question: Airbags reduce average force by increasing: A mass B stopping time C momentum change D speed
Correct Answer: B.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests airbag. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
50. NEET Exam-style Question: Momentum conservation requires net external impulse to be: A zero B maximum C negative D infinite
Correct Answer: A.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external force. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
11
JEE Main Question Bank
50 difficult JEE Main-style momentum questions.
1. JEE Main Exam-style Question: m1=2 kg at 6 m/s sticks to m2=4 kg at rest. Find common speed.
Correct Answer: v=(12)/(6)=2 m/s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
2. JEE Main Exam-style Question: Area under F-t graph is 30 N s for 2 kg body initially at rest. Final speed?
Correct Answer: J=Δp=mv, v=15 m/s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
3. JEE Main Exam-style Question: Bullet 0.02 kg leaves a 2 kg gun at 300 m/s. Recoil speed?
Correct Answer: MV=mv, V=3 m/s opposite bullet.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
4. JEE Main Exam-style Question: Mass 3m at rest breaks into m at 6 m/s and 2m. Velocity of 2m?
Correct Answer: 0=m6+2m v, v=-3 m/s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
5. JEE Main Exam-style Question: Rocket equation with exhaust speed u and mass ratio M0/M=e gives speed gain:
Correct Answer: Δv=u ln(e)=u.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
6. JEE Main Exam-style Question: Masses 1 and 3 kg have velocities 8 and -4 m/s. Total momentum?
Correct Answer: 8-12=-4 kg m/s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
7. JEE Main Exam-style Question: A ball 0.2 kg reverses from 10 to -8 m/s. Magnitude impulse?
Correct Answer: |Δp|=0.2x18=3.6 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
8. JEE Main Exam-style Question: Equal masses exchange velocities in which ideal head-on collision?
Correct Answer: Elastic collision.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
9. JEE Main Exam-style Question: If external impulse acts during collision, total system momentum:
Correct Answer: Changes by external impulse.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
10. JEE Main Exam-style Question: Mass ejection rate r and exhaust speed u give thrust:
Correct Answer: T=ru, ignoring pressure term.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
11. JEE Main Exam-style Question: m1=2 kg at 6 m/s sticks to m2=4 kg at rest. Find common speed.
Correct Answer: v=(12)/(6)=2 m/s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
12. JEE Main Exam-style Question: Area under F-t graph is 30 N s for 2 kg body initially at rest. Final speed?
Correct Answer: J=Δp=mv, v=15 m/s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
13. JEE Main Exam-style Question: Bullet 0.02 kg leaves a 2 kg gun at 300 m/s. Recoil speed?
Correct Answer: MV=mv, V=3 m/s opposite bullet.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
14. JEE Main Exam-style Question: Mass 3m at rest breaks into m at 6 m/s and 2m. Velocity of 2m?
Correct Answer: 0=m6+2m v, v=-3 m/s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
15. JEE Main Exam-style Question: Rocket equation with exhaust speed u and mass ratio M0/M=e gives speed gain:
Correct Answer: Δv=u ln(e)=u.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
16. JEE Main Exam-style Question: Masses 1 and 3 kg have velocities 8 and -4 m/s. Total momentum?
Correct Answer: 8-12=-4 kg m/s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
17. JEE Main Exam-style Question: A ball 0.2 kg reverses from 10 to -8 m/s. Magnitude impulse?
Correct Answer: |Δp|=0.2x18=3.6 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
18. JEE Main Exam-style Question: Equal masses exchange velocities in which ideal head-on collision?
Correct Answer: Elastic collision.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
19. JEE Main Exam-style Question: If external impulse acts during collision, total system momentum:
Correct Answer: Changes by external impulse.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
20. JEE Main Exam-style Question: Mass ejection rate r and exhaust speed u give thrust:
Correct Answer: T=ru, ignoring pressure term.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
21. JEE Main Exam-style Question: m1=2 kg at 6 m/s sticks to m2=4 kg at rest. Find common speed.
Correct Answer: v=(12)/(6)=2 m/s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
22. JEE Main Exam-style Question: Area under F-t graph is 30 N s for 2 kg body initially at rest. Final speed?
Correct Answer: J=Δp=mv, v=15 m/s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
23. JEE Main Exam-style Question: Bullet 0.02 kg leaves a 2 kg gun at 300 m/s. Recoil speed?
Correct Answer: MV=mv, V=3 m/s opposite bullet.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
24. JEE Main Exam-style Question: Mass 3m at rest breaks into m at 6 m/s and 2m. Velocity of 2m?
Correct Answer: 0=m6+2m v, v=-3 m/s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
25. JEE Main Exam-style Question: Rocket equation with exhaust speed u and mass ratio M0/M=e gives speed gain:
Correct Answer: Δv=u ln(e)=u.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
26. JEE Main Exam-style Question: Masses 1 and 3 kg have velocities 8 and -4 m/s. Total momentum?
Correct Answer: 8-12=-4 kg m/s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
27. JEE Main Exam-style Question: A ball 0.2 kg reverses from 10 to -8 m/s. Magnitude impulse?
Correct Answer: |Δp|=0.2x18=3.6 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
28. JEE Main Exam-style Question: Equal masses exchange velocities in which ideal head-on collision?
Correct Answer: Elastic collision.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
29. JEE Main Exam-style Question: If external impulse acts during collision, total system momentum:
Correct Answer: Changes by external impulse.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
30. JEE Main Exam-style Question: Mass ejection rate r and exhaust speed u give thrust:
Correct Answer: T=ru, ignoring pressure term.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
31. JEE Main Exam-style Question: m1=2 kg at 6 m/s sticks to m2=4 kg at rest. Find common speed.
Correct Answer: v=(12)/(6)=2 m/s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
32. JEE Main Exam-style Question: Area under F-t graph is 30 N s for 2 kg body initially at rest. Final speed?
Correct Answer: J=Δp=mv, v=15 m/s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
33. JEE Main Exam-style Question: Bullet 0.02 kg leaves a 2 kg gun at 300 m/s. Recoil speed?
Correct Answer: MV=mv, V=3 m/s opposite bullet.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
34. JEE Main Exam-style Question: Mass 3m at rest breaks into m at 6 m/s and 2m. Velocity of 2m?
Correct Answer: 0=m6+2m v, v=-3 m/s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
35. JEE Main Exam-style Question: Rocket equation with exhaust speed u and mass ratio M0/M=e gives speed gain:
Correct Answer: Δv=u ln(e)=u.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
36. JEE Main Exam-style Question: Masses 1 and 3 kg have velocities 8 and -4 m/s. Total momentum?
Correct Answer: 8-12=-4 kg m/s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
37. JEE Main Exam-style Question: A ball 0.2 kg reverses from 10 to -8 m/s. Magnitude impulse?
Correct Answer: |Δp|=0.2x18=3.6 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
38. JEE Main Exam-style Question: Equal masses exchange velocities in which ideal head-on collision?
Correct Answer: Elastic collision.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
39. JEE Main Exam-style Question: If external impulse acts during collision, total system momentum:
Correct Answer: Changes by external impulse.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
40. JEE Main Exam-style Question: Mass ejection rate r and exhaust speed u give thrust:
Correct Answer: T=ru, ignoring pressure term.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
41. JEE Main Exam-style Question: m1=2 kg at 6 m/s sticks to m2=4 kg at rest. Find common speed.
Correct Answer: v=(12)/(6)=2 m/s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests two-body conservation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
42. JEE Main Exam-style Question: Area under F-t graph is 30 N s for 2 kg body initially at rest. Final speed?
Correct Answer: J=Δp=mv, v=15 m/s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse graph. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
43. JEE Main Exam-style Question: Bullet 0.02 kg leaves a 2 kg gun at 300 m/s. Recoil speed?
Correct Answer: MV=mv, V=3 m/s opposite bullet.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
44. JEE Main Exam-style Question: Mass 3m at rest breaks into m at 6 m/s and 2m. Velocity of 2m?
Correct Answer: 0=m6+2m v, v=-3 m/s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
45. JEE Main Exam-style Question: Rocket equation with exhaust speed u and mass ratio M0/M=e gives speed gain:
Correct Answer: Δv=u ln(e)=u.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
46. JEE Main Exam-style Question: Masses 1 and 3 kg have velocities 8 and -4 m/s. Total momentum?
Correct Answer: 8-12=-4 kg m/s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
47. JEE Main Exam-style Question: A ball 0.2 kg reverses from 10 to -8 m/s. Magnitude impulse?
Correct Answer: |Δp|=0.2x18=3.6 N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
48. JEE Main Exam-style Question: Equal masses exchange velocities in which ideal head-on collision?
Correct Answer: Elastic collision.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
49. JEE Main Exam-style Question: If external impulse acts during collision, total system momentum:
Correct Answer: Changes by external impulse.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests external impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
50. JEE Main Exam-style Question: Mass ejection rate r and exhaust speed u give thrust:
Correct Answer: T=ru, ignoring pressure term.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket thrust. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
12
JEE Advanced Question Bank
50 advanced questions on variable mass, rocket equation, explosions, recoil and multi-particle systems.
1. JEE Advanced Exam-style Question: A rocket ejects mass with relative exhaust speed u. Write ideal velocity gain.
Correct Answer: v=u ln(M0/M).
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
2. JEE Advanced Exam-style Question: Derive small change relation for rocket of mass M ejecting dM.
Correct Answer: M dv = -u dM, integrating gives v=u ln(M0/M).
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
3. JEE Advanced Exam-style Question: A moving shell explodes. What happens to COM path?
Correct Answer: COM follows path decided by external forces, unaffected by internal explosion.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
4. JEE Advanced Exam-style Question: Bullet-gun recoil: compare KE of gun and bullet.
Correct Answer: Momenta equal opposite; lighter bullet gets much larger KE.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
5. JEE Advanced Exam-style Question: Show total momentum P equals Mv_cm.
Correct Answer: By definition v_cm=Σmivi/M, so P=Σmivi=Mv_cm.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
6. JEE Advanced Exam-style Question: Force F=kt acts from 0 to T. Impulse?
Correct Answer: J=∫kt dt=kT²/2.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
7. JEE Advanced Exam-style Question: During short collision, when can weight be ignored?
Correct Answer: When collision time is small so external impulse is negligible.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
8. JEE Advanced Exam-style Question: Three fragments after explosion have vector momenta p1,p2,p3. Condition?
Correct Answer: p1+p2+p3=0.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
9. JEE Advanced Exam-style Question: Why multi-stage rocket helps?
Correct Answer: Discarded empty mass increases effective mass ratio.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
10. JEE Advanced Exam-style Question: Two-dimensional momentum conservation requires:
Correct Answer: Separate conservation of x and y components.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
11. JEE Advanced Exam-style Question: A rocket ejects mass with relative exhaust speed u. Write ideal velocity gain.
Correct Answer: v=u ln(M0/M).
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
12. JEE Advanced Exam-style Question: Derive small change relation for rocket of mass M ejecting dM.
Correct Answer: M dv = -u dM, integrating gives v=u ln(M0/M).
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
13. JEE Advanced Exam-style Question: A moving shell explodes. What happens to COM path?
Correct Answer: COM follows path decided by external forces, unaffected by internal explosion.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
14. JEE Advanced Exam-style Question: Bullet-gun recoil: compare KE of gun and bullet.
Correct Answer: Momenta equal opposite; lighter bullet gets much larger KE.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
15. JEE Advanced Exam-style Question: Show total momentum P equals Mv_cm.
Correct Answer: By definition v_cm=Σmivi/M, so P=Σmivi=Mv_cm.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
16. JEE Advanced Exam-style Question: Force F=kt acts from 0 to T. Impulse?
Correct Answer: J=∫kt dt=kT²/2.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
17. JEE Advanced Exam-style Question: During short collision, when can weight be ignored?
Correct Answer: When collision time is small so external impulse is negligible.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
18. JEE Advanced Exam-style Question: Three fragments after explosion have vector momenta p1,p2,p3. Condition?
Correct Answer: p1+p2+p3=0.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
19. JEE Advanced Exam-style Question: Why multi-stage rocket helps?
Correct Answer: Discarded empty mass increases effective mass ratio.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
20. JEE Advanced Exam-style Question: Two-dimensional momentum conservation requires:
Correct Answer: Separate conservation of x and y components.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
21. JEE Advanced Exam-style Question: A rocket ejects mass with relative exhaust speed u. Write ideal velocity gain.
Correct Answer: v=u ln(M0/M).
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
22. JEE Advanced Exam-style Question: Derive small change relation for rocket of mass M ejecting dM.
Correct Answer: M dv = -u dM, integrating gives v=u ln(M0/M).
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
23. JEE Advanced Exam-style Question: A moving shell explodes. What happens to COM path?
Correct Answer: COM follows path decided by external forces, unaffected by internal explosion.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
24. JEE Advanced Exam-style Question: Bullet-gun recoil: compare KE of gun and bullet.
Correct Answer: Momenta equal opposite; lighter bullet gets much larger KE.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
25. JEE Advanced Exam-style Question: Show total momentum P equals Mv_cm.
Correct Answer: By definition v_cm=Σmivi/M, so P=Σmivi=Mv_cm.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
26. JEE Advanced Exam-style Question: Force F=kt acts from 0 to T. Impulse?
Correct Answer: J=∫kt dt=kT²/2.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
27. JEE Advanced Exam-style Question: During short collision, when can weight be ignored?
Correct Answer: When collision time is small so external impulse is negligible.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
28. JEE Advanced Exam-style Question: Three fragments after explosion have vector momenta p1,p2,p3. Condition?
Correct Answer: p1+p2+p3=0.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
29. JEE Advanced Exam-style Question: Why multi-stage rocket helps?
Correct Answer: Discarded empty mass increases effective mass ratio.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
30. JEE Advanced Exam-style Question: Two-dimensional momentum conservation requires:
Correct Answer: Separate conservation of x and y components.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
31. JEE Advanced Exam-style Question: A rocket ejects mass with relative exhaust speed u. Write ideal velocity gain.
Correct Answer: v=u ln(M0/M).
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
32. JEE Advanced Exam-style Question: Derive small change relation for rocket of mass M ejecting dM.
Correct Answer: M dv = -u dM, integrating gives v=u ln(M0/M).
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
33. JEE Advanced Exam-style Question: A moving shell explodes. What happens to COM path?
Correct Answer: COM follows path decided by external forces, unaffected by internal explosion.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
34. JEE Advanced Exam-style Question: Bullet-gun recoil: compare KE of gun and bullet.
Correct Answer: Momenta equal opposite; lighter bullet gets much larger KE.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
35. JEE Advanced Exam-style Question: Show total momentum P equals Mv_cm.
Correct Answer: By definition v_cm=Σmivi/M, so P=Σmivi=Mv_cm.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
36. JEE Advanced Exam-style Question: Force F=kt acts from 0 to T. Impulse?
Correct Answer: J=∫kt dt=kT²/2.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
37. JEE Advanced Exam-style Question: During short collision, when can weight be ignored?
Correct Answer: When collision time is small so external impulse is negligible.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
38. JEE Advanced Exam-style Question: Three fragments after explosion have vector momenta p1,p2,p3. Condition?
Correct Answer: p1+p2+p3=0.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
39. JEE Advanced Exam-style Question: Why multi-stage rocket helps?
Correct Answer: Discarded empty mass increases effective mass ratio.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
40. JEE Advanced Exam-style Question: Two-dimensional momentum conservation requires:
Correct Answer: Separate conservation of x and y components.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
41. JEE Advanced Exam-style Question: A rocket ejects mass with relative exhaust speed u. Write ideal velocity gain.
Correct Answer: v=u ln(M0/M).
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests variable mass systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
42. JEE Advanced Exam-style Question: Derive small change relation for rocket of mass M ejecting dM.
Correct Answer: M dv = -u dM, integrating gives v=u ln(M0/M).
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket equation. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
43. JEE Advanced Exam-style Question: A moving shell explodes. What happens to COM path?
Correct Answer: COM follows path decided by external forces, unaffected by internal explosion.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion in motion. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
44. JEE Advanced Exam-style Question: Bullet-gun recoil: compare KE of gun and bullet.
Correct Answer: Momenta equal opposite; lighter bullet gets much larger KE.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests recoil with energy. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
45. JEE Advanced Exam-style Question: Show total momentum P equals Mv_cm.
Correct Answer: By definition v_cm=Σmivi/M, so P=Σmivi=Mv_cm.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests multi-particle systems. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
46. JEE Advanced Exam-style Question: Force F=kt acts from 0 to T. Impulse?
Correct Answer: J=∫kt dt=kT²/2.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests impulse integration. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
47. JEE Advanced Exam-style Question: During short collision, when can weight be ignored?
Correct Answer: When collision time is small so external impulse is negligible.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests collision plus impulse. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
48. JEE Advanced Exam-style Question: Three fragments after explosion have vector momenta p1,p2,p3. Condition?
Correct Answer: p1+p2+p3=0.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests explosion at rest. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
49. JEE Advanced Exam-style Question: Why multi-stage rocket helps?
Correct Answer: Discarded empty mass increases effective mass ratio.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests rocket staging. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
50. JEE Advanced Exam-style Question: Two-dimensional momentum conservation requires:
Correct Answer: Separate conservation of x and y components.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
Detailed Explanation: This problem tests vector sign. Choose a sign convention, write momentum as vector quantity, apply impulse or conservation only when the external impulse is negligible, and keep units in kg m/s or N s.
13
IB / IGCSE / A-Level Questions
Separate international banks with answers and explanations.
IB Questions
IB 1. Define linear momentum.
p=mv, a vector in direction of velocity.
IB 2. State impulse-momentum theorem.
Impulse equals change in momentum.
IB 3. What is unit of momentum?
kg m/s.
IB 4. What is unit of impulse?
N s.
IB 5. Why does recoil occur?
Momentum conservation.
IB 6. What is isolated system?
System with zero net external force/impulse.
IB 7. What does area under F-t graph give?
Impulse.
IB 8. Why do airbags reduce force?
They increase stopping time.
IB 9. State rocket equation.
v=u ln(M0/M).
IB 10. What is thrust?
Force due to ejection of mass.
IB 11. Explosion at rest total momentum?
Zero.
IB 12. COM behaviour during explosion?
Unaffected by internal forces.
IB 13. Is momentum scalar?
No, vector.
IB 14. Does KE always conserve in collision?
No.
IB 15. Conservation condition?
Net external impulse zero.
IB 16. Impulse for constant force?
J=FΔt.
IB 17. Impulse for variable force?
J=∫Fdt.
IB 18. Momentum of 3 kg at 4 m/s?
12 kg m/s.
IB 19. Force from impulse?
Favg=J/Δt.
IB 20. Rocket exhaust direction?
Opposite rocket acceleration.
IB 21. Why use signs?
Momentum is vector.
IB 22. Recoil speed depends on gun mass how?
Larger mass means smaller recoil speed.
IB 23. Explosion force is internal or external?
Internal.
IB 24. Momentum graph p-v slope?
Mass.
IB 25. Momentum graph p-m slope?
Velocity.
IGCSE Questions
IGCSE 1. What is momentum?
Mass times velocity.
IGCSE 2. Formula of momentum.
p=mv.
IGCSE 3. Momentum unit.
kg m/s.
IGCSE 4. What is impulse?
Force times time.
IGCSE 5. Impulse unit.
N s.
IGCSE 6. Impulse changes what?
Momentum.
IGCSE 7. Why wear seat belt?
Increase stopping time and reduce force.
IGCSE 8. A 2 kg object at 3 m/s momentum?
6 kg m/s.
IGCSE 9. Two carts stick: use conservation of?
Momentum.
IGCSE 10. Gun recoil direction?
Opposite bullet.
IGCSE 11. Rocket moves by pushing gases where?
Backward.
IGCSE 12. Explosion total momentum if initially rest?
Zero.
IGCSE 13. Momentum is scalar/vector?
Vector.
IGCSE 14. Force-time graph area?
Impulse.
IGCSE 15. Short stopping time gives force?
Large force.
IGCSE 16. Long stopping time gives force?
Small force.
IGCSE 17. External force changes momentum?
Yes.
IGCSE 18. Internal forces alone change total momentum?
No.
IGCSE 19. Car airbag safety concept?
Impulse spread over longer time.
IGCSE 20. Momentum before collision equals after when?
No external force.
IGCSE 21. Speed doubles momentum by factor?
Two.
IGCSE 22. Mass doubles momentum by factor?
Two.
IGCSE 23. Stationary object momentum?
Zero.
IGCSE 24. Balloon motion principle?
Momentum conservation.
IGCSE 25. Cricket bat gives ball what?
Impulse.
A-Level Questions
A-Level 1. Derive J=Δp.
From F=dp/dt, integrate over time.
A-Level 2. Variable force impulse.
J=∫Fdt.
A-Level 3. Rocket equation ideal form.
Δv=u ln(M0/M).
A-Level 4. Thrust with mass flow rate.
T=u dm/dt.
A-Level 5. External impulse relation.
Jext=ΔPsystem.
A-Level 6. COM momentum relation.
P=Mvcm.
A-Level 7. 2D conservation equations.
Conserve x and y components separately.
A-Level 8. Recoil KE distribution.
KE larger for smaller mass for same momentum.
A-Level 9. Explosion in moving frame.
Total momentum remains initial momentum.
A-Level 10. Airbag force relation.
Favg=Δp/Δt.
A-Level 11. Momentum dimensions.
MLT^-1.
A-Level 12. Impulse dimensions.
MLT^-1.
A-Level 13. Rocket mass ratio significance.
Larger M0/M gives larger Δv.
A-Level 14. Perfectly inelastic collision.
Bodies stick; momentum conserved if isolated.
A-Level 15. Elastic collision.
Momentum and KE conserved.
A-Level 16. Why momentum conservation survives internal forces?
Newton third-law pairs cancel.
A-Level 17. When conservation fails?
Significant external impulse.
A-Level 18. Ball-wall impulse magnitude with e.
J=m(1+e)u for fixed wall.
A-Level 19. p-v graph slope.
Mass.
A-Level 20. p-m graph slope.
Velocity.
A-Level 21. F-t rectangular area.
FΔt.
A-Level 22. F-t triangular area.
1/2 base height.
A-Level 23. Jet propulsion principle.
Momentum conservation.
A-Level 24. Rocket staging benefit.
Improves mass ratio.
A-Level 25. Explosion energy source.
Internal chemical energy.
14
Assertion Reason
30 assertion-reason questions.
1. Assertion: Momentum is a vector. Reason: Velocity is a vector.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
2. Assertion: Impulse equals change in momentum. Reason: F=dp/dt.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
3. Assertion: Airbag reduces average force. Reason: It increases stopping time.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
4. Assertion: Momentum is always conserved in every collision. Reason: Internal forces cancel.
Answer: Assertion false; external impulse may act.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
5. Assertion: Gun recoils backward. Reason: Initial momentum of bullet-gun system is zero.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
6. Assertion: Rocket can move in vacuum. Reason: It pushes exhaust gases backward.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
7. Assertion: Explosion changes COM motion by internal forces. Reason: Internal forces are very large.
Answer: Assertion false; reason true but irrelevant.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
8. Assertion: Area under F-t graph gives impulse. Reason: Impulse is ∫Fdt.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
9. Assertion: Momentum direction is same as acceleration. Reason: p=mv.
Answer: Assertion false; momentum direction is velocity direction.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
10. Assertion: Rocket equation uses changing mass. Reason: Rocket is a variable mass system.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
11. Assertion: Momentum is a vector. Reason: Velocity is a vector.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
12. Assertion: Impulse equals change in momentum. Reason: F=dp/dt.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
13. Assertion: Airbag reduces average force. Reason: It increases stopping time.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
14. Assertion: Momentum is always conserved in every collision. Reason: Internal forces cancel.
Answer: Assertion false; external impulse may act.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
15. Assertion: Gun recoils backward. Reason: Initial momentum of bullet-gun system is zero.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
16. Assertion: Rocket can move in vacuum. Reason: It pushes exhaust gases backward.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
17. Assertion: Explosion changes COM motion by internal forces. Reason: Internal forces are very large.
Answer: Assertion false; reason true but irrelevant.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
18. Assertion: Area under F-t graph gives impulse. Reason: Impulse is ∫Fdt.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
19. Assertion: Momentum direction is same as acceleration. Reason: p=mv.
Answer: Assertion false; momentum direction is velocity direction.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
20. Assertion: Rocket equation uses changing mass. Reason: Rocket is a variable mass system.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
21. Assertion: Momentum is a vector. Reason: Velocity is a vector.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
22. Assertion: Impulse equals change in momentum. Reason: F=dp/dt.
Answer: Both true; reason explains assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
23. Assertion: Airbag reduces average force. Reason: It increases stopping time.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
24. Assertion: Momentum is always conserved in every collision. Reason: Internal forces cancel.
Answer: Assertion false; external impulse may act.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
25. Assertion: Gun recoils backward. Reason: Initial momentum of bullet-gun system is zero.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
26. Assertion: Rocket can move in vacuum. Reason: It pushes exhaust gases backward.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
27. Assertion: Explosion changes COM motion by internal forces. Reason: Internal forces are very large.
Answer: Assertion false; reason true but irrelevant.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
28. Assertion: Area under F-t graph gives impulse. Reason: Impulse is ∫Fdt.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
29. Assertion: Momentum direction is same as acceleration. Reason: p=mv.
Answer: Assertion false; momentum direction is velocity direction.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
30. Assertion: Rocket equation uses changing mass. Reason: Rocket is a variable mass system.
Answer: Both true.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
Explanation: Decide truth of assertion and reason, then whether the reason explains the assertion.
15
Case Study Questions
Rocket launch, recoil, airbag safety, explosion and conservation cases.
Case Study: Rocket launch
Passage: A rocket ejects hot gases downward. Questions: thrust direction, role of exhaust speed, mass ratio, staging and rocket equation.
Answers and Explanations: Momentum conservation gives upward thrust. Ideal speed gain is u ln(M0/M). Staging improves mass ratio.
Answers and Explanations: Momentum conservation gives upward thrust. Ideal speed gain is u ln(M0/M). Staging improves mass ratio.
Case Study: Recoil of gun
Passage: A bullet leaves a gun at high speed. Questions: recoil direction, momentum conservation, recoil speed, energy distribution and safety.
Answers and Explanations: Gun momentum equals bullet momentum in opposite direction. Heavy gun has small recoil speed.
Answers and Explanations: Gun momentum equals bullet momentum in opposite direction. Heavy gun has small recoil speed.
Case Study: Airbag safety
Passage: A passenger is stopped during collision. Questions: impulse, stopping time, average force, energy loss and why airbag helps.
Answers and Explanations: Impulse is same momentum change; larger time means smaller average force.
Answers and Explanations: Impulse is same momentum change; larger time means smaller average force.
Case Study: Explosion problems
Passage: A body explodes into fragments. Questions: total momentum, fragment directions, COM motion, energy change and external impulse.
Answers and Explanations: Momentum is conserved if external impulse is negligible; KE can increase due to internal energy.
Answers and Explanations: Momentum is conserved if external impulse is negligible; KE can increase due to internal energy.
Case Study: Momentum conservation
Passage: Two carts collide on a smooth track. Questions: common speed, isolated system, signs, external force and collision type.
Answers and Explanations: Use total momentum before equals after; assign directions carefully.
Answers and Explanations: Use total momentum before equals after; assign directions carefully.
16
Common Student Mistakes
Fix these before attempting NEET/JEE momentum numericals.
Force vs Momentum
Force changes momentum; it is not momentum itself.
Impulse vs Force
Impulse depends on both force and time.
Wrong Sign Convention
Choose positive direction before substituting velocities.
Ignoring Vector Direction
Momentum conservation is vector conservation.
External Force Present
Use momentum conservation only when external impulse is zero or negligible.
Rocket Equation Mistakes
Use mass ratio M0/M and exhaust speed relative to rocket.
Explosion Misconceptions
KE can increase, but total momentum still follows external impulse.
Searching for a Physics Tutor? If Momentum, Recoil, Rocket Motion, Explosions or NEET/JEE numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com