Angular displacement
Angular displacement θ measures how much the radius vector turns.
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C6
CLASS 11 PHYSICS • LAWS OF MOTION
Circular Motion and Dynamics
Master centripetal force, banking, conical pendulum, vertical circle, loops and circular-motion numericals.
CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
Section 1
Circular Motion
Circular motion is motion along a circular path. Uniform circular motion has constant speed but changing velocity direction. Non-uniform circular motion has changing speed and therefore tangential acceleration too.
Angular velocity
ω = dθ/dt. For uniform circular motion, angular velocity is constant.
Angular acceleration
α = dω/dt. It appears when angular velocity changes.
v = rω
an = v2/r = rω2
Section 2
Centripetal Force
Centripetal force is the net inward force required to keep a body moving in a circle. It is always directed toward the centre.
F = mac = m(v2/r)
F = mv2/r
F = mrω2
Source can be tension
For a stone tied to a string, tension provides centripetal force.
Source can be friction
For a car turning on a road, friction may provide centripetal force.
Source can be gravity
For satellites, gravity provides centripetal force.
Section 3
Centrifugal Force
Centrifugal force is an apparent outward force used only in a rotating non-inertial frame. It is not a real interaction force in an inertial frame.
| Point | Centripetal Force | Centrifugal Force |
|---|---|---|
| Frame | Inertial frame | Rotating non-inertial frame |
| Direction | Toward centre | Away from centre |
| Nature | Real net force | Apparent pseudo force |
| Use | Newton equations in ground frame | Equilibrium in rotating frame |
Section 4
Banking of Roads
Banking tilts the road so a component of normal reaction supplies centripetal force. This reduces dependence on friction.
N cos θ = mg
N sin θ = mv2/r
tan θ = v2/rg
Frictionless banking
Only normal and weight act. The horizontal component of normal is centripetal.
Banking with friction
Friction acts up or down the slope depending on whether the vehicle tends to slip down or up the bank.
Special cases
At design speed, friction is not required. Below design speed friction acts up the slope; above design speed friction acts down the slope.
Section 5
Conical Pendulum
In a conical pendulum, the bob moves in a horizontal circle while the string makes a constant angle with the vertical.
T cos θ = mg
T sin θ = mv2/r
tan θ = v2/rg
v = √(rg tan θ)
Time period: P = 2π√(l cos θ/g)
Section 6
Vertical Circular Motion
In a vertical circle, speed and tension vary with position because gravity changes potential energy and radial force balance.
At top: T + mg = mv2/r
At bottom: T - mg = mv2/r
At side: T = mv2/r
Minimum velocity at top: vtop = √(gr)
Minimum velocity at bottom: vbottom = √(5gr)
Energy: 1/2 mv2 + mgh = constant
Section 7
Loop Problems
Loop problems use vertical circular motion. For contact at the top, normal reaction must not become negative.
At top of loop: N + mg = mv2/r
Minimum top speed: v = √(gr)
Minimum bottom speed for full loop: v = √(5gr)
Roller coaster
At the top, passengers need enough speed to maintain contact.
Bead in circular track
Normal force changes with position and may become zero at limiting contact.
Car in vertical circle
Use radial equation at top, bottom and side separately.
Section 8
Important Graphs
θ vs t
θ vs t helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
ω vs t
ω vs t helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
v vs t
v vs t helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
aₙ vs v
aₙ vs v helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
aₙ vs r
aₙ vs r helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
aₙ vs ω
aₙ vs ω helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
Uniform circular motion graphs
Uniform circular motion graphs helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
Non-uniform circular motion graphs
Non-uniform circular motion graphs helps identify whether angular speed, speed or centripetal acceleration is constant or changing.
Section 9
High-Quality Numericals
CBSE NumericalShow Answer
Question: A 2 kg body moves in a circle of radius 1 m with speed 5 m/s. Find centripetal force.
Given: m=2 kg, r=1 m, v=5 m/s
Formula: F=mv²/r
Calculation: F=2×25/1=50 N
Final Answer: 50 N toward centre
Exam Tip: Direction is as important as magnitude.
NEET NumericalShow Answer
Question: A road is banked at angle θ for speed v. Derive relation.
Given: frictionless banking
Formula: tanθ=v²/rg
Calculation: Divide N sinθ=mv²/r by N cosθ=mg.
Final Answer: tanθ=v²/rg
Exam Tip: Use components of normal reaction.
JEE Main NumericalShow Answer
Question: A conical pendulum has radius r and angle θ. Find speed.
Given: r, θ, g
Formula: tanθ=v²/rg
Calculation: v²=rg tanθ.
Final Answer: v=√(rg tanθ)
Exam Tip: Use horizontal component of tension.
JEE Advanced NumericalShow Answer
Question: Find minimum bottom speed for complete vertical circle.
Given: radius r
Formula: v_bottom=√(5gr)
Calculation: At top v²=gr and energy drop from bottom to top is 2mg r.
Final Answer: √(5gr)
Exam Tip: Top tension is zero at limiting condition.
IB NumericalShow Answer
Question: Explain why velocity changes in uniform circular motion.
Given: constant speed circle
Formula: velocity is vector
Calculation: Direction changes continuously even if magnitude is constant.
Final Answer: Acceleration exists toward centre.
Exam Tip: Do not confuse speed and velocity.
IGCSE NumericalShow Answer
Question: Why does a car need friction while turning on a flat road?
Given: flat circular turn
Formula: friction provides mv²/r
Calculation: Static friction acts toward centre.
Final Answer: Friction is centripetal force.
Exam Tip: Friction is sideways, not backward always.
A-Level NumericalShow Answer
Question: A loop-the-loop has radius r. Minimum top speed?
Given: radius r
Formula: v_top=√(gr)
Calculation: At top, N=0 at limiting contact, so mg=mv²/r.
Final Answer: √(gr)
Exam Tip: Normal cannot pull the car inward.
Section 10
NEET Question Bank
NEET Exam-style Question 1Show Answer
Question: NEET 1: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 2Show Answer
Question: NEET 2: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 3Show Answer
Question: NEET 3: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 4Show Answer
Question: NEET 4: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 5Show Answer
Question: NEET 5: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 6Show Answer
Question: NEET 6: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 7Show Answer
Question: NEET 7: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 8Show Answer
Question: NEET 8: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 9Show Answer
Question: NEET 9: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 10Show Answer
Question: NEET 10: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 11Show Answer
Question: NEET 11: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 12Show Answer
Question: NEET 12: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 13Show Answer
Question: NEET 13: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 14Show Answer
Question: NEET 14: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 15Show Answer
Question: NEET 15: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 16Show Answer
Question: NEET 16: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 17Show Answer
Question: NEET 17: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 18Show Answer
Question: NEET 18: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 19Show Answer
Question: NEET 19: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 20Show Answer
Question: NEET 20: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 21Show Answer
Question: NEET 21: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 22Show Answer
Question: NEET 22: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 23Show Answer
Question: NEET 23: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 24Show Answer
Question: NEET 24: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 25Show Answer
Question: NEET 25: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 26Show Answer
Question: NEET 26: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 27Show Answer
Question: NEET 27: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 28Show Answer
Question: NEET 28: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 29Show Answer
Question: NEET 29: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 30Show Answer
Question: NEET 30: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 31Show Answer
Question: NEET 31: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 32Show Answer
Question: NEET 32: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 33Show Answer
Question: NEET 33: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 34Show Answer
Question: NEET 34: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 35Show Answer
Question: NEET 35: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 36Show Answer
Question: NEET 36: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 37Show Answer
Question: NEET 37: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 38Show Answer
Question: NEET 38: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 39Show Answer
Question: NEET 39: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 40Show Answer
Question: NEET 40: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 41Show Answer
Question: NEET 41: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 42Show Answer
Question: NEET 42: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 43Show Answer
Question: NEET 43: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 44Show Answer
Question: NEET 44: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 45Show Answer
Question: NEET 45: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
NEET Exam-style Question 46Show Answer
Question: NEET 46: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
NEET Exam-style Question 47Show Answer
Question: NEET 47: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
NEET Exam-style Question 48Show Answer
Question: NEET 48: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
NEET Exam-style Question 49Show Answer
Question: NEET 49: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
NEET Exam-style Question 50Show Answer
Question: NEET 50: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
Section 11
JEE Main Question Bank
JEE Main Exam-style Question 1Show Answer
Question: JEE Main 1: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 2Show Answer
Question: JEE Main 2: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 3Show Answer
Question: JEE Main 3: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 4Show Answer
Question: JEE Main 4: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 5Show Answer
Question: JEE Main 5: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 6Show Answer
Question: JEE Main 6: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 7Show Answer
Question: JEE Main 7: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 8Show Answer
Question: JEE Main 8: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 9Show Answer
Question: JEE Main 9: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 10Show Answer
Question: JEE Main 10: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 11Show Answer
Question: JEE Main 11: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 12Show Answer
Question: JEE Main 12: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 13Show Answer
Question: JEE Main 13: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 14Show Answer
Question: JEE Main 14: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 15Show Answer
Question: JEE Main 15: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 16Show Answer
Question: JEE Main 16: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 17Show Answer
Question: JEE Main 17: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 18Show Answer
Question: JEE Main 18: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 19Show Answer
Question: JEE Main 19: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 20Show Answer
Question: JEE Main 20: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 21Show Answer
Question: JEE Main 21: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 22Show Answer
Question: JEE Main 22: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 23Show Answer
Question: JEE Main 23: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 24Show Answer
Question: JEE Main 24: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 25Show Answer
Question: JEE Main 25: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 26Show Answer
Question: JEE Main 26: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 27Show Answer
Question: JEE Main 27: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 28Show Answer
Question: JEE Main 28: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 29Show Answer
Question: JEE Main 29: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 30Show Answer
Question: JEE Main 30: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 31Show Answer
Question: JEE Main 31: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 32Show Answer
Question: JEE Main 32: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 33Show Answer
Question: JEE Main 33: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 34Show Answer
Question: JEE Main 34: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 35Show Answer
Question: JEE Main 35: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 36Show Answer
Question: JEE Main 36: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 37Show Answer
Question: JEE Main 37: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 38Show Answer
Question: JEE Main 38: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 39Show Answer
Question: JEE Main 39: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 40Show Answer
Question: JEE Main 40: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 41Show Answer
Question: JEE Main 41: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 42Show Answer
Question: JEE Main 42: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 43Show Answer
Question: JEE Main 43: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 44Show Answer
Question: JEE Main 44: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 45Show Answer
Question: JEE Main 45: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 46Show Answer
Question: JEE Main 46: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 47Show Answer
Question: JEE Main 47: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 48Show Answer
Question: JEE Main 48: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 49Show Answer
Question: JEE Main 49: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
JEE Main Exam-style Question 50Show Answer
Question: JEE Main 50: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
Section 12
JEE Advanced Question Bank
JEE Advanced Exam-style Question 1Show Answer
Question: JEE Advanced 1: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 2Show Answer
Question: JEE Advanced 2: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 3Show Answer
Question: JEE Advanced 3: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 4Show Answer
Question: JEE Advanced 4: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 5Show Answer
Question: JEE Advanced 5: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 6Show Answer
Question: JEE Advanced 6: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 7Show Answer
Question: JEE Advanced 7: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 8Show Answer
Question: JEE Advanced 8: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 9Show Answer
Question: JEE Advanced 9: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 10Show Answer
Question: JEE Advanced 10: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 11Show Answer
Question: JEE Advanced 11: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 12Show Answer
Question: JEE Advanced 12: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 13Show Answer
Question: JEE Advanced 13: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 14Show Answer
Question: JEE Advanced 14: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 15Show Answer
Question: JEE Advanced 15: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 16Show Answer
Question: JEE Advanced 16: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 17Show Answer
Question: JEE Advanced 17: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 18Show Answer
Question: JEE Advanced 18: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 19Show Answer
Question: JEE Advanced 19: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 20Show Answer
Question: JEE Advanced 20: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 21Show Answer
Question: JEE Advanced 21: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 22Show Answer
Question: JEE Advanced 22: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 23Show Answer
Question: JEE Advanced 23: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 24Show Answer
Question: JEE Advanced 24: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 25Show Answer
Question: JEE Advanced 25: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 26Show Answer
Question: JEE Advanced 26: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 27Show Answer
Question: JEE Advanced 27: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 28Show Answer
Question: JEE Advanced 28: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 29Show Answer
Question: JEE Advanced 29: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 30Show Answer
Question: JEE Advanced 30: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 31Show Answer
Question: JEE Advanced 31: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 32Show Answer
Question: JEE Advanced 32: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 33Show Answer
Question: JEE Advanced 33: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 34Show Answer
Question: JEE Advanced 34: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 35Show Answer
Question: JEE Advanced 35: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 36Show Answer
Question: JEE Advanced 36: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 37Show Answer
Question: JEE Advanced 37: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 38Show Answer
Question: JEE Advanced 38: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 39Show Answer
Question: JEE Advanced 39: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 40Show Answer
Question: JEE Advanced 40: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 41Show Answer
Question: JEE Advanced 41: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 42Show Answer
Question: JEE Advanced 42: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 43Show Answer
Question: JEE Advanced 43: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 44Show Answer
Question: JEE Advanced 44: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 45Show Answer
Question: JEE Advanced 45: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 46Show Answer
Question: JEE Advanced 46: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 47Show Answer
Question: JEE Advanced 47: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 48Show Answer
Question: JEE Advanced 48: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 49Show Answer
Question: JEE Advanced 49: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
JEE Advanced Exam-style Question 50Show Answer
Question: JEE Advanced 50: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
Section 13
IB / IGCSE / A-Level Questions
IB Questions
IB Exam-style Question 1Show Answer
Question: IB 1: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 2Show Answer
Question: IB 2: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 3Show Answer
Question: IB 3: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 4Show Answer
Question: IB 4: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 5Show Answer
Question: IB 5: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 6Show Answer
Question: IB 6: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 7Show Answer
Question: IB 7: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 8Show Answer
Question: IB 8: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 9Show Answer
Question: IB 9: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 10Show Answer
Question: IB 10: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 11Show Answer
Question: IB 11: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 12Show Answer
Question: IB 12: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 13Show Answer
Question: IB 13: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 14Show Answer
Question: IB 14: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 15Show Answer
Question: IB 15: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 16Show Answer
Question: IB 16: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 17Show Answer
Question: IB 17: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 18Show Answer
Question: IB 18: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 19Show Answer
Question: IB 19: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 20Show Answer
Question: IB 20: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 21Show Answer
Question: IB 21: Why is centripetal force not a new force?
Correct Answer: It is the name of the required inward net force, supplied by tension, friction, gravity or normal reaction.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 22Show Answer
Question: IB 22: What force provides centripetal force in banking?
Correct Answer: Horizontal component of normal reaction, with friction if present.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 23Show Answer
Question: IB 23: What is top condition in vertical circle?
Correct Answer: T + mg = mv²/r, and minimum speed occurs when T=0.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 24Show Answer
Question: IB 24: How is conical pendulum solved?
Correct Answer: Resolve tension: T cosθ=mg and T sinθ=mv²/r.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IB Exam-style Question 25Show Answer
Question: IB 25: What is radius of curvature use?
Correct Answer: Use a_n=v²/R where R is instantaneous radius of curvature.
Detailed Explanation: Draw radial direction first, then write net radial force = mv²/r.
IGCSE Questions
IGCSE Exam-style Question 1Show Answer
Question: IGCSE 1: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
IGCSE Exam-style Question 2Show Answer
Question: IGCSE 2: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
IGCSE Exam-style Question 3Show Answer
Question: IGCSE 3: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
IGCSE Exam-style Question 4Show Answer
Question: IGCSE 4: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
IGCSE Exam-style Question 5Show Answer
Question: IGCSE 5: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
IGCSE Exam-style Question 6Show Answer
Question: IGCSE 6: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
IGCSE Exam-style Question 7Show Answer
Question: IGCSE 7: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
IGCSE Exam-style Question 8Show Answer
Question: IGCSE 8: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
IGCSE Exam-style Question 9Show Answer
Question: IGCSE 9: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
IGCSE Exam-style Question 10Show Answer
Question: IGCSE 10: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
IGCSE Exam-style Question 11Show Answer
Question: IGCSE 11: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
IGCSE Exam-style Question 12Show Answer
Question: IGCSE 12: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
IGCSE Exam-style Question 13Show Answer
Question: IGCSE 13: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
IGCSE Exam-style Question 14Show Answer
Question: IGCSE 14: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
IGCSE Exam-style Question 15Show Answer
Question: IGCSE 15: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
IGCSE Exam-style Question 16Show Answer
Question: IGCSE 16: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
IGCSE Exam-style Question 17Show Answer
Question: IGCSE 17: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
IGCSE Exam-style Question 18Show Answer
Question: IGCSE 18: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
IGCSE Exam-style Question 19Show Answer
Question: IGCSE 19: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
IGCSE Exam-style Question 20Show Answer
Question: IGCSE 20: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
IGCSE Exam-style Question 21Show Answer
Question: IGCSE 21: Centripetal acceleration is directed?
Options: (A) tangentially (B) towards centre (C) away from centre (D) vertically down
Correct Answer: B
Detailed Explanation: Centripetal acceleration always points toward the centre.
IGCSE Exam-style Question 22Show Answer
Question: IGCSE 22: For circular motion, F equals?
Options: (A) mv/r (B) mv²/r (C) mr/v (D) mvr
Correct Answer: B
Detailed Explanation: Centripetal force is mv²/r.
IGCSE Exam-style Question 23Show Answer
Question: IGCSE 23: Frictionless banking satisfies?
Options: (A) tanθ=v²/rg (B) tanθ=rg/v² (C) sinθ=v²/rg (D) cosθ=v²/rg
Correct Answer: A
Detailed Explanation: Divide horizontal and vertical equations.
IGCSE Exam-style Question 24Show Answer
Question: IGCSE 24: Minimum top speed in vertical circle is?
Options: (A) √gr (B) √2gr (C) √3gr (D) √5gr
Correct Answer: A
Detailed Explanation: At top, mg supplies centripetal force at limiting contact.
IGCSE Exam-style Question 25Show Answer
Question: IGCSE 25: Centrifugal force is?
Options: (A) real in inertial frame (B) apparent in rotating frame (C) gravity (D) normal reaction
Correct Answer: B
Detailed Explanation: It is a pseudo force in non-inertial frame.
A-Level Questions
A-Level Exam-style Question 1Show Answer
Question: A-Level 1: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 2Show Answer
Question: A-Level 2: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 3Show Answer
Question: A-Level 3: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 4Show Answer
Question: A-Level 4: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 5Show Answer
Question: A-Level 5: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 6Show Answer
Question: A-Level 6: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 7Show Answer
Question: A-Level 7: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 8Show Answer
Question: A-Level 8: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 9Show Answer
Question: A-Level 9: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 10Show Answer
Question: A-Level 10: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 11Show Answer
Question: A-Level 11: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 12Show Answer
Question: A-Level 12: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 13Show Answer
Question: A-Level 13: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 14Show Answer
Question: A-Level 14: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 15Show Answer
Question: A-Level 15: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 16Show Answer
Question: A-Level 16: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 17Show Answer
Question: A-Level 17: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 18Show Answer
Question: A-Level 18: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 19Show Answer
Question: A-Level 19: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 20Show Answer
Question: A-Level 20: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 21Show Answer
Question: A-Level 21: In a vertical circle, why is bottom tension maximum?
Correct Answer: At bottom, T - mg = mv²/r and speed is highest by energy conservation.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 22Show Answer
Question: A-Level 22: A bead loses contact in a loop. What condition decides it?
Correct Answer: Normal reaction becomes zero.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 23Show Answer
Question: A-Level 23: In banking with friction, why are two limiting speeds possible?
Correct Answer: Friction reverses direction depending on whether vehicle tends to slip up or down the bank.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 24Show Answer
Question: A-Level 24: In non-uniform circular motion, what accelerations exist?
Correct Answer: Radial acceleration v²/r and tangential acceleration dv/dt.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
A-Level Exam-style Question 25Show Answer
Question: A-Level 25: For loop minimum height, what is used?
Correct Answer: Energy plus top condition v²=gr.
Detailed Explanation: Use radial force equation at the chosen point and energy conservation between points.
Section 14
Assertion Reason
Assertion-Reason 1Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 2Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 3Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 4Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 5Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 6Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 7Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 8Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 9Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 10Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 11Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 12Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 13Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 14Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 15Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 16Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 17Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 18Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 19Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 20Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 21Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 22Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 23Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 24Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 25Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 26Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 27Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 28Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 29Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Assertion-Reason 30Show Answer
Question: Assertion: In uniform circular motion, speed is constant but acceleration is not zero. Reason: Direction of velocity changes continuously.
Answer: Both are true, and the reason correctly explains the assertion.
Explanation: Acceleration is the rate of change of velocity vector, not only speed.
Section 15
Case Study Questions
Banking of roads
Passage: A vehicle turns safely because the road is inclined and normal reaction has a horizontal component.
Banking of roads Case Question 1Show Answer
Question: What is the key circular-motion idea in banking of roads question 1?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Banking of roads Case Question 2Show Answer
Question: What is the key circular-motion idea in banking of roads question 2?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Banking of roads Case Question 3Show Answer
Question: What is the key circular-motion idea in banking of roads question 3?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Banking of roads Case Question 4Show Answer
Question: What is the key circular-motion idea in banking of roads question 4?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Roller coaster
Passage: At the top of a loop, contact is maintained only if speed is high enough.
Roller coaster Case Question 1Show Answer
Question: What is the key circular-motion idea in roller coaster question 1?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Roller coaster Case Question 2Show Answer
Question: What is the key circular-motion idea in roller coaster question 2?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Roller coaster Case Question 3Show Answer
Question: What is the key circular-motion idea in roller coaster question 3?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Roller coaster Case Question 4Show Answer
Question: What is the key circular-motion idea in roller coaster question 4?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Conical pendulum
Passage: The bob moves in a horizontal circle due to the horizontal component of tension.
Conical pendulum Case Question 1Show Answer
Question: What is the key circular-motion idea in conical pendulum question 1?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Conical pendulum Case Question 2Show Answer
Question: What is the key circular-motion idea in conical pendulum question 2?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Conical pendulum Case Question 3Show Answer
Question: What is the key circular-motion idea in conical pendulum question 3?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Conical pendulum Case Question 4Show Answer
Question: What is the key circular-motion idea in conical pendulum question 4?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Vertical circle
Passage: Tension varies at top, side and bottom because both speed and weight component change.
Vertical circle Case Question 1Show Answer
Question: What is the key circular-motion idea in vertical circle question 1?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Vertical circle Case Question 2Show Answer
Question: What is the key circular-motion idea in vertical circle question 2?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Vertical circle Case Question 3Show Answer
Question: What is the key circular-motion idea in vertical circle question 3?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Vertical circle Case Question 4Show Answer
Question: What is the key circular-motion idea in vertical circle question 4?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Satellite circular motion
Passage: Gravity provides centripetal force for orbital motion.
Satellite circular motion Case Question 1Show Answer
Question: What is the key circular-motion idea in satellite circular motion question 1?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Satellite circular motion Case Question 2Show Answer
Question: What is the key circular-motion idea in satellite circular motion question 2?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Satellite circular motion Case Question 3Show Answer
Question: What is the key circular-motion idea in satellite circular motion question 3?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Satellite circular motion Case Question 4Show Answer
Question: What is the key circular-motion idea in satellite circular motion question 4?
Answer: Identify centre, draw inward radial direction, then apply net radial force = mv²/r.
Detailed explanation: Use the force actually pointing toward centre; do not invent centripetal force as an extra force.
Section 16
Common Student Mistakes
Confusing centripetal and centrifugal force
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Wrong force direction
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Using mv²/r incorrectly
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Forgetting tension variation
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Banking sign errors
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Vertical circle misconceptions
Fix: Mark the centre first, draw real forces, resolve radial direction, then use net radial force = mv²/r.
Final Quality Check
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Circular motion explained
Centripetal force derived
Centrifugal force explained
Banking of roads derived
Conical pendulum derived
Vertical circular motion derived
Loop problems included
Correct graphs included
50 NEET questions included
50 JEE Main questions included
50 JEE Advanced questions included
IB / IGCSE / A-Level sections included
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