Searching for a Physics Tutor? If Newton's Law of Gravitation, Vector Form, Extended Body Gravitation or NEET/JEE numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com
Universal Law of Gravitation
Master Newton's law of gravitation, gravitational constant, vector form, force between particles, extended bodies, numericals and PYQs.
Newton's Law of Gravitation
Newton proposed that every particle in the universe attracts every other particle with a force along the line joining their centres. This law is universal because it applies to apples near Earth, the Earth-Moon system, planets around the Sun and stars in galaxies.
The gravitational force is always attractive. It increases when either mass increases and decreases rapidly when the separation increases.
Earth and Moon
Two Masses
Planet and Satellite
Gravitational Constant G
The constant G tells how strong gravitational interaction is in nature. It is very small, so gravitational force between ordinary classroom objects is negligible, but it becomes important for planets, moons and stars.
Value
G = 6.67 x 10-11 N m2 kg-2
Unit and Dimensions
SI unit: N m2 kg-2. Dimensions: [M-1L3T-2].
Cavendish Experiment
Cavendish used a torsion balance to measure the tiny attraction between lead spheres, allowing the value of G and Earth's mass to be estimated.
Vector Form of Gravitational Force
For two point masses, vector form gives both magnitude and direction. If r vector points from m1 to m2, the force on m1 due to m2 is opposite to the chosen outward direction when written with the negative sign.
Meaning of Symbols
- r is the position vector joining the masses.
- r is the magnitude of r.
- r is the unit vector along r.
- The negative sign represents attraction.
Vector Diagram
Force Between Particles
For point masses, use the centre-to-centre distance directly. In multiple-particle systems, calculate individual force vectors first and then add them vectorially.
Example 1
Two 5 kg masses are 2 m apart. Find force.
Show Answer
Example 2
If distance doubles, what happens to gravitational force?
Show Answer
Example 3
Two equal forces act at right angles on a particle. Find net force.
Show Answer
Force Between Extended Bodies
For spherical bodies, gravitation often becomes simple because of symmetry. A uniform spherical body attracts an outside particle as if its entire mass were concentrated at its centre.
Shell Theorem
- Outside a uniform spherical shell: field and force are as if total mass is at the centre.
- Inside a uniform spherical shell: net gravitational field is zero.
- At the centre: force is zero by symmetry.
Uniform Solid Sphere
- Outside: behaves as a point mass at centre.
- Inside: only the mass enclosed within that radius contributes to field.
- For two spheres outside each other, use centre-to-centre distance.
Shell Outside
Shell Inside
Two Extended Spheres
Searching for a Physics Tutor? If Newton's Law of Gravitation, Vector Form, Extended Body Gravitation or NEET/JEE numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com
Applications
1. Earth-Moon Attraction
Concept: Mutual gravitational pull keeps the Moon bound to Earth.
Formula: F = GMm/r2.
Exam Tip: Use Earth-Moon centre distance, not surface distance.
2. Planet-Sun Attraction
Concept: Solar gravity provides centripetal force for planets.
Formula: GMm/r2 = mv2/r.
Exam Tip: Cancel planet mass when finding orbital speed.
3. Artificial Satellites
Concept: Gravity supplies centripetal force.
Formula: v = sqrt(GM/r).
Exam Tip: r = R + h for altitude h.
4. Binary Stars
Concept: Two stars revolve around their common centre of mass.
Formula: F = Gm1m2/r2.
Exam Tip: Both stars have same angular speed.
5. Orbital Motion
Concept: Gravity bends the path continuously.
Formula: T2 proportional to r3.
Exam Tip: Link universal gravitation with Kepler's third law.
6. Falling Bodies
Concept: Near Earth, gravitational force appears as weight.
Formula: W = mg.
Exam Tip: g is local field strength, not universal constant.
7. Tides
Concept: Difference in lunar gravitational pull across Earth creates tides.
Formula: Tidal effect depends on distance strongly.
Exam Tip: Tides are due to variation of force, not only total force.
8. Planetary Motion
Concept: Gravity explains elliptical planetary orbits.
Formula: F = GMm/r2.
Exam Tip: At smaller r, force is larger.
9. Escape Velocity Connection
Concept: Escape energy comes from gravitational potential energy.
Formula: ve = sqrt(2GM/R).
Exam Tip: Escape velocity is independent of projectile mass.
10. Weight Variation with Altitude
Concept: Weight decreases when distance from Earth's centre increases.
Formula: g' = GM/(R+h)2.
Exam Tip: Use R+h, not h alone.
Important Graphs
F vs r
Force decreases non-linearly as distance increases because F is proportional to 1/r2.
F vs r2
As r2 increases, F decreases inversely: F proportional to 1/r2.
F vs 1/r2
This graph is a straight line through origin because F = Gm1m2(1/r2).
Important Formula Table
| Topic | Formula / Result | Use |
|---|---|---|
| Newton's Law | F = Gm1m2/r2 | Force between two point masses. |
| Vector Form | F12 = -Gm1m2 r/r3 | Direction-sensitive force calculation. |
| Unit of G | N m2 kg-2 | SI unit from force law. |
| Dimensions of G | [M-1L3T-2] | Dimensional analysis. |
| Shell Outside | F = GMm/r2 | Shell behaves as point mass at centre. |
| Shell Inside | F = 0 | Net field inside uniform spherical shell. |
| Solid Sphere Outside | F = GMm/r2 | Spherical body acts from centre. |
| Force Ratio | F2/F1 = (m'1m'2/m1m2)(r12/r22) | Fast ratio problems. |
| Orbital Connection | GMm/r2 = mv2/r | Satellite and planetary motion. |
High-Quality Solved Numericals
CBSE 1
Question: Two bodies of 10 kg and 20 kg are 5 m apart. Find F.
Show Answer
Given: m1=10 kg, m2=20 kg, r=5 m. Formula: F=Gm1m2/r2. Calculation: F=6.67 x 10-11 x 200/25 = 5.34 x 10-10 N. Final Answer: 5.34 x 10-10 N. Exam Tip: Keep powers of ten separate. Common Mistake: Using r instead of r2.
CBSE 2
Question: If both masses are doubled and distance is doubled, find new force in terms of F.
Show Answer
Given: m1'=2m1, m2'=2m2, r'=2r. Formula: F proportional to m1m2/r2. Calculation: F'=(2 x 2)/(22)F=F. Final Answer: unchanged. Tip: Ratio method is fastest. Mistake: Forgetting distance is squared.
NEET 1
Question: Distance becomes one-third. What is force?
Show Answer
Formula: F proportional to 1/r2. Calculation: F' = F/(1/3)2 = 9F. Final Answer: 9F. Tip: Inverse square law. Mistake: Answering 3F.
NEET 2
Question: A 2 kg mass feels 8 x 10-10 N due to a 6 kg mass. Find r.
Show Answer
Given: F=8 x 10-10 N. Formula: r=sqrt(Gm1m2/F). Calculation: r=sqrt(6.67 x 10-11 x 12/(8 x 10-10)) about 1.0 m. Final Answer: about 1 m. Tip: Rearrange before substituting. Mistake: Missing square root.
JEE Main 1
Question: Three equal masses form an equilateral triangle of side a. Find net force on one mass.
Show Answer
Given: each force F=Gm2/a2, angle=60 degrees. Formula: R=sqrt(F2+F2+2F2cos60). Calculation: R=sqrt(3)F. Final Answer: sqrt(3)Gm2/a2. Tip: Use vector addition. Mistake: Adding magnitudes as 2F.
JEE Main 2
Question: Four equal masses are at square corners. Find force on one corner mass.
Show Answer
Given: side a. Adjacent forces are F=Gm2/a2; diagonal force is F/2. Calculation: x and y components each = F + F/(2sqrt2). Final Answer: R=sqrt2 F + F/2 = (sqrt2 + 1/2)Gm2/a2. Tip: Resolve diagonal force. Mistake: Using diagonal distance as a.
JEE Advanced 1
Question: A particle is inside a uniform spherical shell. Find net gravitational force.
Show Answer
Given: uniform shell. Formula: Shell theorem. Calculation: contributions from all shell elements cancel. Final Answer: zero. Tip: Valid everywhere inside. Mistake: Treating shell as point mass at centre for inside point.
IB / A-Level
Question: Why is G called universal?
Show Answer
Answer: It has the same value for any pair of masses anywhere, independent of medium, mass type or location. Exam Tip: Do not confuse universal G with local g.
NEET Question Bank
Authentic years are mentioned only when known; otherwise these are NEET exam-style questions.
NEET Exam-style Question 1
What is the dimensional formula of G?
Show Answer
NEET Exam-style Question 2
If r is doubled, F becomes?
Show Answer
NEET Exam-style Question 3
If each mass is tripled, F becomes?
Show Answer
NEET Exam-style Question 4
Gravitational force is always what type?
Show Answer
NEET Exam-style Question 5
SI unit of G is?
Show Answer
NEET Exam-style Question 6
Inside a uniform spherical shell, field is?
Show Answer
NEET Exam-style Question 7
Outside a uniform shell, it behaves as?
Show Answer
NEET Exam-style Question 8
Force between 1 kg and 1 kg at 1 m is?
Show Answer
NEET Exam-style Question 9
Which experiment measured G?
Show Answer
NEET Exam-style Question 10
When distance becomes half, force becomes?
Show Answer
NEET Exam-style Question 11
If one mass is doubled and the other halved, force becomes?
Show Answer
NEET Exam-style Question 12
Force acts along which line?
Show Answer
NEET Exam-style Question 13
G depends on medium: true or false?
Show Answer
NEET Exam-style Question 14
Why ordinary objects do not attract visibly?
Show Answer
NEET Exam-style Question 15
For two equal masses, forces on them are?
Show Answer
NEET Exam-style Question 16
F vs 1/r2 graph is?
Show Answer
NEET Exam-style Question 17
F vs r graph is?
Show Answer
NEET Exam-style Question 18
For extended spheres outside each other, distance used is?
Show Answer
NEET Exam-style Question 19
Can gravitational force be repulsive?
Show Answer
NEET Exam-style Question 20
What happens to F if r becomes 3r?
Show Answer
NEET Exam-style Question 21
If masses become 2m and 3m, force factor is?
Show Answer
NEET Exam-style Question 22
Unit vector in vector form gives what?
Show Answer
NEET Exam-style Question 23
Negative sign in vector form means?
Show Answer
NEET Exam-style Question 24
Net force at centre of a uniform shell is?
Show Answer
NEET Exam-style Question 25
Net field anywhere inside uniform shell is?
Show Answer
NEET Exam-style Question 26
If F=16 N at r, force at 4r is?
Show Answer
NEET Exam-style Question 27
If F=9 N at r, force at r/3 is?
Show Answer
NEET Exam-style Question 28
Gravitational force follows which law with distance?
Show Answer
NEET Exam-style Question 29
Does G change from Earth to Moon?
Show Answer
NEET Exam-style Question 30
Does g change from Earth to Moon?
Show Answer
NEET Exam-style Question 31
Which is larger, G or g numerically near Earth?
Show Answer
NEET Exam-style Question 32
For a point outside a sphere, where is mass assumed?
Show Answer
NEET Exam-style Question 33
What is the force on a particle due to two equal opposite symmetric masses?
Show Answer
NEET Exam-style Question 34
Two forces F at 60 degrees have resultant?
Show Answer
NEET Exam-style Question 35
Two forces F at 90 degrees have resultant?
Show Answer
NEET Exam-style Question 36
Two equal opposite gravitational forces can cancel at a point?
Show Answer
NEET Exam-style Question 37
What provides centripetal force for satellites?
Show Answer
NEET Exam-style Question 38
For orbital motion, GMm/r2 equals?
Show Answer
NEET Exam-style Question 39
Planet mass cancels in orbital speed formula around Sun?
Show Answer
NEET Exam-style Question 40
Force between two bodies is 10 N. Distance doubled and one mass doubled. New force?
Show Answer
NEET Exam-style Question 41
Force between particles is central because?
Show Answer
NEET Exam-style Question 42
Can shell theorem be applied to non-uniform shell directly?
Show Answer
NEET Exam-style Question 43
Which distance is used for Earth-satellite force?
Show Answer
NEET Exam-style Question 44
Force on m due to M equals force on M due to m?
Show Answer
NEET Exam-style Question 45
Acceleration produced by those equal forces is same?
Show Answer
NEET Exam-style Question 46
What is point mass approximation?
Show Answer
NEET Exam-style Question 47
Does gravitational force require contact?
Show Answer
NEET Exam-style Question 48
F is proportional to which mass quantity?
Show Answer
NEET Exam-style Question 49
If r increases by 10%, force approximately changes how?
Show Answer
NEET Exam-style Question 50
The law of gravitation is valid for which scale?
Show Answer
JEE Main Question Bank
JEE Main 1
Three equal masses are at vertices of an equilateral triangle. Net force on one?
Show Answer
JEE Main 2
Four equal masses at square corners; force on one corner?
Show Answer
JEE Main 3
Two masses M and 4M are distance d apart. Where is zero field?
Show Answer
JEE Main 4
If F at r is F0, find F at r plus r.
Show Answer
JEE Main 5
Masses at x=0 and x=a are M and M. Field at midpoint?
Show Answer
JEE Main 6
Masses M, M at x=0, a. Field at x=2a direction?
Show Answer
JEE Main 7
Two 10 kg masses 1 m apart: order of force?
Show Answer
JEE Main 8
Find G dimension using F = GmM/r2.
Show Answer
JEE Main 9
If density of two equal spheres doubles and radius unchanged, force factor at same separation?
Show Answer
JEE Main 10
If radii of two same-density spheres double and separation of centres doubles, force factor?
Show Answer
JEE Main 11
Force at surface of sphere on mass m?
Show Answer
JEE Main 12
Force on particle at centre of uniform shell?
Show Answer
JEE Main 13
Force on particle outside shell at distance 2R from centre?
Show Answer
JEE Main 14
Particle exactly midway between masses M and 9M separated by d. Net field?
Show Answer
JEE Main 15
Two equal forces F at 120 degrees resultant?
Show Answer
JEE Main 16
Three equal masses on a line at -a, 0, +a. Force on middle?
Show Answer
JEE Main 17
Force on left mass in three equal collinear masses spaced a?
Show Answer
JEE Main 18
Mass at each cube corner; direction of force on one corner mass?
Show Answer
JEE Main 19
F vs 1/r2 slope equals?
Show Answer
JEE Main 20
For same force, if one mass is quadrupled, distance must become?
Show Answer
JEE Main 21
Two masses M and 2M. Forces are equal?
Show Answer
JEE Main 22
Accelerations of M and 2M due to mutual force ratio?
Show Answer
JEE Main 23
If G were doubled, orbital speed around same planet would change by?
Show Answer
JEE Main 24
Field outside sphere varies as?
Show Answer
JEE Main 25
Field inside uniform shell varies as?
Show Answer
JEE Main 26
A shell and point mass outside: use what distance?
Show Answer
JEE Main 27
Why gravitational force is conservative?
Show Answer
JEE Main 28
Two masses at perpendicular directions from a point produce equal fields. Resultant?
Show Answer
JEE Main 29
At what distance from M between M and 4M is field zero?
Show Answer
JEE Main 30
At what distance from 4M is that point?
Show Answer
JEE Main 31
Two spheres touch externally. Centre distance?
Show Answer
JEE Main 32
Two identical spheres touch. Force?
Show Answer
JEE Main 33
If separation is very large compared to size, bodies can be treated as?
Show Answer
JEE Main 34
Net force on centre mass in square with equal masses at corners?
Show Answer
JEE Main 35
Net field at centre of regular polygon with equal masses at vertices?
Show Answer
JEE Main 36
One vertex mass removed from square. Field at centre direction?
Show Answer
JEE Main 37
Force is 100 N at r. At 10r?
Show Answer
JEE Main 38
Force is 100 N at r. At r/10?
Show Answer
JEE Main 39
For F constant, if both masses become 4 times, r must become?
Show Answer
JEE Main 40
Can the centre of mass be outside a binary star pair?
Show Answer
JEE Main 41
Gravitational field due to point mass points?
Show Answer
JEE Main 42
Force on point mass due to shell from outside points?
Show Answer
JEE Main 43
Field at a point due to multiple particles is found by?
Show Answer
JEE Main 44
Force law is inverse square due to?
Show Answer
JEE Main 45
What graph linearizes Newton's law?
Show Answer
JEE Main 46
In vector form, why r3 appears?
Show Answer
JEE Main 47
Two masses at same point idealization leads force to?
Show Answer
JEE Main 48
Can gravitational shielding occur in Newtonian gravity?
Show Answer
JEE Main 49
If F is measured for known masses and distance, G equals?
Show Answer
JEE Main 50
Why is gravity important despite small G?
Show Answer
JEE Advanced Question Bank
These problems focus on vector gravitation, shell theorem, extended bodies, multiple particle systems and scaling.
JEE Advanced 1
Three masses m, 2m, 3m lie at x=0, a, 2a. Find force on 2m.
Show Answer
JEE Advanced 2
At centre of a square, one of four equal corner masses is removed. Field magnitude?
Show Answer
JEE Advanced 3
A point mass is inside a uniform spherical shell at distance R/2 from centre. Force?
Show Answer
JEE Advanced 4
A point mass is outside shell at 3R. Force?
Show Answer
JEE Advanced 5
Two identical solid spheres radius R touch. Force between them?
Show Answer
JEE Advanced 6
Two masses M and 4M separated by d. Locate zero field.
Show Answer
JEE Advanced 7
Two equal masses at (a,0) and (-a,0). Field at (0,y)?
Show Answer
JEE Advanced 8
Equal masses at (0,a), (0,-a), (a,0), (-a,0). Field at origin?
Show Answer
JEE Advanced 9
One mass removed from the previous arrangement. Field at origin?
Show Answer
JEE Advanced 10
A ring-like approximation is not covered by shell theorem. What method is needed?
Show Answer
JEE Advanced 11
Two bodies attract with F. Densities same, radii doubled, separation same. New F?
Show Answer
JEE Advanced 12
If radii doubled and centre separation also doubled?
Show Answer
JEE Advanced 13
Why does a uniform shell exert zero force inside?
Show Answer
JEE Advanced 14
Force on a particle just inside a shell surface?
Show Answer
JEE Advanced 15
Force just outside a shell surface?
Show Answer
JEE Advanced 16
Why is there discontinuity at shell surface for field?
Show Answer
JEE Advanced 17
For a uniform solid sphere, field at radius r inside is proportional to?
Show Answer
JEE Advanced 18
At centre of a uniform solid sphere, field?
Show Answer
JEE Advanced 19
At surface of uniform solid sphere, field?
Show Answer
JEE Advanced 20
At 2R outside solid sphere, field?
Show Answer
JEE Advanced 21
Two forces of magnitudes 3F and 4F at right angle. Resultant?
Show Answer
JEE Advanced 22
Three equal forces separated by 120 degrees. Resultant?
Show Answer
JEE Advanced 23
Masses at vertices of regular hexagon. Field at centre?
Show Answer
JEE Advanced 24
One vertex mass removed from regular hexagon. Field at centre?
Show Answer
JEE Advanced 25
For two masses M and nM, zero field location from M?
Show Answer
JEE Advanced 26
Show vector force has inverse square magnitude.
Show Answer
JEE Advanced 27
If r vector is reversed, what happens to force direction?
Show Answer
JEE Advanced 28
Two equal masses on x-axis; field at far point x much greater than a?
Show Answer
JEE Advanced 29
What assumption fails when bodies overlap?
Show Answer
JEE Advanced 30
Can external gravitational field of a non-spherical body always be point-like?
Show Answer
JEE Advanced 31
A dumbbell of two equal masses is far away. Approximate field?
Show Answer
JEE Advanced 32
Two masses approach due to gravity. Which quantity is conserved?
Show Answer
JEE Advanced 33
Why are equal and opposite forces not canceling motion of two-body system?
Show Answer
JEE Advanced 34
Two masses M and 4M are released. Acceleration ratio initially?
Show Answer
JEE Advanced 35
Force ratio for distances r, 2r, 3r?
Show Answer
JEE Advanced 36
If F at r is F, average of forces at r and 2r?
Show Answer
JEE Advanced 37
Two particles at same distance from test mass with angle theta. Resultant?
Show Answer
JEE Advanced 38
For theta = 120 degrees in previous problem?
Show Answer
JEE Advanced 39
For theta = 60 degrees?
Show Answer
JEE Advanced 40
Why centre-to-centre distance matters for spheres?
Show Answer
JEE Advanced 41
A particle at cavity centre inside a spherical shell feels?
Show Answer
JEE Advanced 42
Mass distribution symmetric about a point gives field at point?
Show Answer
JEE Advanced 43
Force between two planets if masses and distance are all scaled by factor k?
Show Answer
JEE Advanced 44
Force between two same-density planets if radii scale by k and gap scales by k?
Show Answer
JEE Advanced 45
For equal density spheres touching, force scales with radius how?
Show Answer
JEE Advanced 46
What is the gravitational force direction on a satellite?
Show Answer
JEE Advanced 47
If satellite velocity is tangential, gravity is perpendicular to velocity for circular orbit. Work done?
Show Answer
JEE Advanced 48
Can gravitational force change speed in elliptical orbit?
Show Answer
JEE Advanced 49
Why use vector method in multi-particle gravitation?
Show Answer
JEE Advanced 50
What is the most common advanced-level shell theorem trap?
Show Answer
IB / IGCSE / A-Level Questions
25 IB Questions
- Define gravitational force.
Show Answer
Attractive force between masses. - State Newton's law.
Show Answer
F=Gm1m2/r2. - Explain why G is universal.
Show Answer
It is the same for all masses everywhere. - Give SI unit of G.
Show Answer
N m2 kg-2. - What is meant by inverse square law?
Show Answer
Quantity varies as 1/r2. - Why use centre distance?
Show Answer
Spherical bodies act from centres externally. - Describe Cavendish experiment.
Show Answer
Torsion balance measured tiny attraction between masses. - Distinguish G and g.
Show Answer
G is universal constant; g is local field strength. - Force when distance doubles?
Show Answer
One-fourth. - Force when mass doubles?
Show Answer
Doubles if other factors unchanged. - Why is gravity weak in lab?
Show Answer
G is very small. - What is a field force?
Show Answer
A force acting without contact. - State shell theorem inside result.
Show Answer
Zero field inside uniform shell. - State shell theorem outside result.
Show Answer
Acts as mass at centre. - What graph proves inverse square?
Show Answer
F vs 1/r2 straight line. - Why force is mutual?
Show Answer
Newton's third law. - Does medium affect G?
Show Answer
No. - What causes tides?
Show Answer
Variation in Moon's gravitational pull across Earth. - What holds satellites?
Show Answer
Gravitational force. - Can gravity repel?
Show Answer
No in Newtonian model. - What is a point mass?
Show Answer
Body treated as if mass is concentrated at a point. - When is point approximation valid?
Show Answer
When size is small compared to separation. - What is central force?
Show Answer
Force along line joining centres. - Why vector form is useful?
Show Answer
It includes direction and magnitude. - Give one application.
Show Answer
Planetary motion, satellites or tides.
25 IGCSE Questions
- What is gravity?
Show Answer
Attraction between masses. - What happens to gravity with distance?
Show Answer
It decreases. - What happens when mass increases?
Show Answer
Gravitational force increases. - Is gravity contact or non-contact?
Show Answer
Non-contact. - Which force keeps Moon in orbit?
Show Answer
Gravity. - What is weight?
Show Answer
Gravitational force on a mass. - Formula for weight?
Show Answer
W=mg. - What is field strength?
Show Answer
Force per unit mass. - Unit of gravitational field strength?
Show Answer
N kg-1. - Why planets orbit Sun?
Show Answer
Sun's gravity provides centripetal force. - Force at double distance?
Show Answer
One-fourth for inverse square law. - Force at half distance?
Show Answer
Four times. - Can gravity act in vacuum?
Show Answer
Yes. - Does bigger mass attract more?
Show Answer
Yes. - What is satellite?
Show Answer
Object orbiting a planet. - Name natural satellite of Earth.
Show Answer
Moon. - Why do objects fall?
Show Answer
Earth attracts them gravitationally. - What is centre-to-centre distance?
Show Answer
Distance between centres of two bodies. - Does mass change on Moon?
Show Answer
No. - Does weight change on Moon?
Show Answer
Yes. - What is orbital path?
Show Answer
Path followed by a satellite or planet. - What is G?
Show Answer
Universal gravitational constant. - Why is G small important?
Show Answer
Lab gravitational forces are tiny. - Gravity between people exists?
Show Answer
Yes, but extremely small. - Give one practical use.
Show Answer
Satellite motion or weighing objects.
25 A-Level Questions
- Derive dimensions of G.
Show Answer
From G=Fr2/mM, dimensions are [M-1L3T-2]. - Explain vector form.
Show Answer
F vector equals -GmM r vector/r3. - Why negative sign?
Show Answer
Attraction opposite the outward separation vector. - State superposition principle.
Show Answer
Net field/force is vector sum of individual contributions. - Find zero field between M and 9M.
Show Answer
d/(1+3)=d/4 from M. - Field inside shell?
Show Answer
Zero. - Field outside shell?
Show Answer
GM/r2. - Uniform sphere outside field?
Show Answer
GM/r2. - Uniform sphere inside field dependence?
Show Answer
Proportional to r. - Why use integration for non-spherical bodies?
Show Answer
Symmetry is insufficient for point-mass replacement. - Two equal fields at angle theta resultant?
Show Answer
2E cos(theta/2). - What is gravitational potential link?
Show Answer
Field is negative gradient of potential. - Why field is radial for point mass?
Show Answer
Spherical symmetry. - What is inverse square graph linear variable?
Show Answer
1/r2. - What did Cavendish measure?
Show Answer
G using torsion balance. - How does force scale with density?
Show Answer
For fixed volume, proportional to product of densities. - For fixed density and radius scaling k, mass scales?
Show Answer k3. - For fixed density touching spheres, force scales?
Show Answer R4. - Why internal forces cancel for system momentum?
Show Answer
They are equal and opposite pairs. - What remains conserved in isolated two-body attraction?
Show Answer
Total momentum and energy. - Field at centre of symmetric mass ring?
Show Answer
Zero. - Field at centre of regular polygon equal masses?
Show Answer
Zero. - One mass removed from symmetric set?
Show Answer
Net equals negative of removed contribution. - When Newtonian law fails significantly?
Show Answer
Very strong gravity or relativistic conditions. - Why still use Newtonian gravitation?
Show Answer
It is accurate for most school-level planetary and satellite problems.
Assertion Reason Questions
AR 1
Assertion: G is universal. Reason: Its value is independent of medium.
Show Answer
AR 2
Assertion: Gravity is always attractive. Reason: Mass is always positive in Newtonian gravitation.
Show Answer
AR 3
Assertion: Force becomes one-fourth when distance doubles. Reason: Force varies inversely with distance.
Show Answer
AR 4
Assertion: Inside a uniform shell field is zero. Reason: Opposite shell elements cancel exactly.
Show Answer
AR 5
Assertion: Outside a shell it acts as point mass. Reason: Spherical symmetry permits shell theorem.
Show Answer
AR 6
Assertion: G and g are same. Reason: Both are used in gravitation.
Show Answer
AR 7
Assertion: Gravitational force is central. Reason: It acts along line joining centres.
Show Answer
AR 8
Assertion: Equal mutual forces give equal accelerations. Reason: Newton's third law holds.
Show Answer
AR 9
Assertion: F vs 1/r2 is linear. Reason: F=GmM(1/r2).
Show Answer
AR 10
Assertion: Point mass approximation is always valid. Reason: All masses have centres.
Show Answer
AR 11
Assertion: Shell theorem applies to uniform spherical shells. Reason: Symmetry is essential.
Show Answer
AR 12
Assertion: Gravity can act through vacuum. Reason: It is a field interaction.
Show Answer
AR 13
Assertion: Cavendish measured G. Reason: Torsion balance detects tiny force.
Show Answer
AR 14
Assertion: At centre of uniform sphere field is zero. Reason: Symmetric mass pulls equally in all directions.
Show Answer
AR 15
Assertion: For two spheres outside each other, use surface gap. Reason: Force acts at surfaces.
Show Answer
AR 16
Assertion: Negative sign in vector form shows attraction. Reason: Force is opposite to chosen separation vector.
Show Answer
AR 17
Assertion: Gravitational force is conservative. Reason: Potential energy can be defined.
Show Answer
AR 18
Assertion: A larger mass exerts larger force on smaller mass than smaller exerts on larger. Reason: Larger mass has more inertia.
Show Answer
AR 19
Assertion: Satellite is held by gravity. Reason: Gravity supplies centripetal force.
Show Answer
AR 20
Assertion: F decreases with distance. Reason: Gravitational influence spreads over spherical area.
Show Answer
AR 21
Assertion: G has same dimensions as g. Reason: Both contain letter g.
Show Answer
AR 22
Assertion: Net force at midpoint of equal masses is zero. Reason: Forces are equal and opposite.
Show Answer
AR 23
Assertion: Net field at centre of square equal corner masses is zero. Reason: Diagonal pairs cancel.
Show Answer
AR 24
Assertion: If one square corner mass is removed, field remains zero. Reason: Three masses are still symmetric.
Show Answer
AR 25
Assertion: Formula F=GmM/r2 is scalar magnitude. Reason: Direction needs vector notation.
Show Answer
AR 26
Assertion: Field inside solid sphere is zero everywhere. Reason: Shell theorem says inside shell field is zero.
Show Answer
AR 27
Assertion: Field outside solid sphere is point-like. Reason: It can be considered as layers of shells.
Show Answer
AR 28
Assertion: G is difficult to measure. Reason: Gravitational force between lab masses is tiny.
Show Answer
AR 29
Assertion: F vs r2 is inverse curve. Reason: F proportional to 1/r2.
Show Answer
AR 30
Assertion: Gravity is responsible for tides. Reason: Lunar gravitational pull varies across Earth.
Show Answer
Case Study Questions
Earth-Moon System
Passage: Earth and Moon attract each other with equal and opposite gravitational forces. The same attraction provides the centripetal force for the Moon's orbital motion.
- Which force keeps Moon in orbit?
- Are Earth and Moon forces equal?
- Which distance is used?
Show Answer
Answers: Gravity; yes, equal and opposite; centre-to-centre distance. Explanation: Newton's law and third law apply simultaneously, while orbital calculation uses separation between centres.
Planetary Motion
Passage: A planet moves around the Sun because solar gravity continuously changes the direction of its velocity.
- Write the gravitational force formula.
- What provides centripetal force?
- What happens when r decreases?
Show Answer
Answers: F=GMm/r2; gravity; force increases. Explanation: Universal gravitation links planetary orbit with centripetal motion.
Artificial Satellites
Passage: A satellite at altitude h moves around Earth in a near circular orbit.
- What is orbital radius?
- Which force acts inward?
- Does satellite mass cancel in speed formula?
Show Answer
Answers: R+h; gravitational force; yes. Explanation: GMm/(R+h)2 = mv2/(R+h), so m cancels.
Shell Theorem
Passage: A uniform spherical shell has mass M and radius R. A particle may be placed outside or inside it.
- Outside result?
- Inside result?
- Most common mistake?
Show Answer
Answers: Outside behaves as point mass at centre; inside field zero; using outside formula inside. Explanation: Shell theorem depends on whether point is inside or outside.
Extended Body Gravitation
Passage: Two uniform spherical planets attract each other from far apart.
- Can each be treated as point mass?
- Where is mass assumed?
- Which distance enters formula?
Show Answer
Answers: Yes, externally; at centre; centre-to-centre distance. Explanation: Spherical symmetry allows point-mass replacement outside the bodies.
Common Student Mistakes
Confusing G and g
G is universal constant; g is local gravitational field strength or acceleration due to gravity.
Wrong Distance Usage
Use centre-to-centre distance, especially for planets, satellites and extended spheres.
Surface Distance Error
For two spherical bodies, do not use the gap between surfaces unless the formula has been rewritten in terms of it.
Vector Sign Mistakes
The negative sign in vector form tells attractive direction; it is not a negative magnitude.
Shell Theorem Misconceptions
Outside shell behaves as point mass, but inside a uniform shell field is zero.
Extended Body Assumptions
Point-mass replacement is exact for spherical symmetry outside the body, not for every irregular object.
Searching for a Physics Tutor? If Newton's Law of Gravitation, Vector Form, Extended Body Gravitation or NEET/JEE numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com