Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G m₁ m₂ / r², directed along the line joining them. G ≈ 6.67 × 10⁻¹¹ N·m²/kg².
-- NCERT Class 11 Physics, Ch. 7, p. 130Universal Law Gravitation
8 MCQs3 revision cards9-step worked example
Source: NCERT GravitationOfficial key: NTA-verifiedLast updated: 25 Sep 2026
Universal Law Gravitation, explained for NEET
Newton's law of universal gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres (NCERT Class 11 Physics Chapter 7, page 130):
F = G m₁ m₂ / r²
Here G = 6.674 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant, measured by Cavendish. The force is always attractive, acts along the line joining the two centres, and obeys Newton's third law — both bodies experience equal and opposite forces regardless of their mass difference.
Key features to lock in:
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Inverse-square dependence on distance. The force falls as 1/r², not 1/r. Doubling the centre-to-centre distance reduces the force to one-quarter, not one-half.
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Product of masses, not sum. If one mass doubles, the force doubles. If both double, the force quadruples.
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Centre-to-centre distance for spheres. For uniform spheres, r is measured from centre to centre (shell theorem), not surface to surface. A common error is using the gap between surfaces instead of the full centre-to-centre separation.
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Superposition. The net gravitational force on a body due to multiple masses is the vector sum of individual pairwise forces.
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G versus g. G is a universal constant (same everywhere). g (acceleration due to gravity at a planet's surface) is derived from it: g = GM/R². They are not interchangeable.
The law applies to point masses and, by the shell theorem, to any spherically symmetric mass distribution — the condition NEET problems almost always assume. When a problem says "uniform sphere," you can treat it as a point mass at its centre.
Can you answer these Universal Law Gravitation MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The SI unit of the universal gravitational constant G is:
Show answer and why every option is right or wrong
Answer: C. From F = Gm₁m₂/r², rearranging gives G = Fr²/(m₁m₂). Units: N·m²/kg² (NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because it has m instead of m². Since G = Fr²/(m₁m₂), the distance term contributes m², not m.
Why B is wrong: B is wrong because it inverts the mass and distance placement. G has kg² in the denominator and m² in the numerator, not the reverse.
Why D is wrong: D is wrong because the denominator must be kg² (product of two masses), not kg.
MCQ 2Easy RecallPractice
Newton's law of gravitation applies exactly (without shell-theorem extension) to:
Show answer and why every option is right or wrong
Answer: A. The law in its basic form F = Gm₁m₂/r² is stated for point masses. Extension to spheres requires the shell theorem (NCERT Class 11 Physics Chapter 7, page 130).
Why B is wrong: B is wrong because cubes are not spherically symmetric; the basic point-mass formula does not directly apply to extended non-spherical bodies.
Why C is wrong: C is wrong because a cube lacks spherical symmetry, so the point-mass formula cannot be directly applied to the sphere-cube pair without integration.
Why D is wrong: D is wrong because cylinders are not spherically symmetric; applying the point-mass formula requires the bodies to be either point masses or uniform spheres.
MCQ 3Easy RecallPractice
The gravitational force between two bodies is always:
Show answer and why every option is right or wrong
Answer: C. Gravitational force is always attractive between any two masses, regardless of their magnitudes (NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because gravity is never repulsive. Unlike electrostatic or magnetic forces, gravitational force has no sign reversal — mass is always positive.
Why B is wrong: B is wrong because the attractive nature of gravity does not depend on the magnitude of the masses. All masses attract all other masses.
Why D is wrong: D is wrong because the force is never zero as long as both masses are nonzero. A large mass ratio simply means one body accelerates far less than the other (Newton's third law still gives equal forces).
MCQ 4Direct ApplicationPractice
Two identical spheres, each of mass m, are separated by a centre-to-centre distance d. The gravitational force between them is F. If the distance is halved to d/2, the new force is:
Show answer and why every option is right or wrong
Answer: B. F ∝ 1/r². Halving r increases the force by a factor of (1/(1/2))² = 4. New force = 4F (NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because it treats the force as directly proportional to r (halving r → halving F). The actual dependence is inverse-square.
Why C is wrong: C is wrong because it applies 1/r² in the wrong direction — reducing r by half increases the force, not decreases it.
Why D is wrong: D is wrong because it uses an inverse-first-power relationship (F ∝ 1/r). The correct law is F ∝ 1/r².
MCQ 5Direct ApplicationPractice
Two spheres of masses M and 4M are separated by a centre-to-centre distance d. The ratio of the gravitational force on M due to 4M, to the force on 4M due to M, is:
Show answer and why every option is right or wrong
Answer: C. C is correct. Gravitation acts as a third-law pair: the two forces are equal in magnitude and opposite in direction, whatever the masses. Both are GM(4M)/d² = 4GM²/d², so the ratio is 1 : 1. The product of the masses appears in the formula once, and it is the same product for both bodies. What DOES differ is the resulting acceleration — the lighter sphere accelerates four times as hard (NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because 1 : 4 assumes each body's force is set by its own mass, so the smaller one feels less. Both forces contain the same product M × 4M; it is the acceleration, not the force, that the body's own mass divides.
Why B is wrong: B is wrong because 4 : 1 is the same error with the ratio the other way up — attributing the larger force to the larger mass.
Why D is wrong: D is wrong because 1 : 16 squares the mass ratio, as if the force depended on M² for one body and (4M)² for the other. The force is linear in each mass and identical for the pair.
MCQ 6Direct ApplicationPractice
The gravitational force between two uniform spheres is F when their surfaces are in contact. Each sphere has radius R. If the spheres are moved apart so that there is a gap of 2R between their surfaces, the new force is:
Show answer and why every option is right or wrong
Answer: A. When surfaces touch, centre-to-centre distance = R + R = 2R. With a 2R gap, centre-to-centre distance = R + 2R + R = 4R. Force ratio = (2R)²/(4R)² = 1/4. New force = F/4 (applying F = Gm₁m₂/r² with r measured centre-to-centre per the shell theorem, NCERT Class 11 Physics Chapter 7, page 130).
Why B is wrong: B is wrong because it adds each sphere's diameter to the gap, taking the centre-to-centre distance as 2R + 2R + 2R = 6R, three times the original 2R. From centre to surface is R, so the distance is R + 2R + R = 4R.
Why C is wrong: C is wrong because F/16 squares the ratio twice: (2R/4R)² = 1/4 is already the inverse-square factor, and squaring it again gives 1/16.
Why D is wrong: D is wrong because it assumes a linear (1/r) relationship instead of inverse-square (1/r²). Doubling the centre-to-centre distance gives 1/4 the force, not 1/2.
MCQ 7Concept TrapPractice
Gravitational force between two bodies depends on the intervening medium:
Show answer and why every option is right or wrong
Answer: B. Unlike electric force, gravitational force cannot be shielded or altered by any intervening medium. F = Gm₁m₂/r² has no permittivity-like factor (NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because gravitational force has no medium-dependent factor. The formula F = Gm₁m₂/r² contains no permittivity or permeability term that could introduce medium dependence.
Why C is wrong: C is wrong because gravitational force is the same in vacuum, air, water, or any other medium. There is no analogue to the dielectric constant for gravity.
Why D is wrong: D is wrong because gravitational force penetrates all materials. There is no gravitational shielding — unlike electromagnetic fields, gravity cannot be blocked by conductors or any known material.
MCQ 8CalculationPractice
Three identical particles, each of mass m, are placed at the vertices of an equilateral triangle of side a. The magnitude of the net gravitational force on any one particle is:
Show answer and why every option is right or wrong
Answer: D. Each particle feels two forces, each of magnitude F₀ = Gm²/a². The angle between these two force vectors is 60°. By vector addition: F_net = √(F₀² + F₀² + 2F₀²cos60°) = √(2F₀² + 2F₀² × 1/2) = √(3F₀²) = √3 Gm²/a² (applying F = Gm₁m₂/r² twice and then the parallelogram law, NCERT Class 11 Physics Chapter 7, page 130).
Why A is wrong: A is wrong because it accounts for only one of the two pairwise forces. The particle is attracted by both other vertices, and the forces must be added vectorially.
Why B is wrong: B is wrong because it simply doubles the pairwise force (scalar addition). The two force vectors are at 60°, not 0°, so their resultant is √3 F₀, not 2F₀.
Why C is wrong: C is wrong because it triples the pairwise force, as if all three forces pointed in the same direction. Only two forces act on each particle, and they are at 60° — the resultant is √3 F₀.
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Universal Law Gravitation: quick recall before you leave
How do you solve a Universal Law Gravitation question? A worked example
Pattern: Direct application of F = Gm₁m₂/r² — force calculation between two bodies. (No topic-specific PYQ pattern survived Rule 7 filtering; all four dossier patterns belong to other topics. This worked example is constructed from the universal gravitation formula and the NCERT law entry.)
- 1
Given
Two uniform spheres: mass of sphere A = 5.0 × 10⁴ kg, mass of sphere B = 3.0 × 10⁴ kg. Centre-to-centre separation = 2.0 m.
- 2
Required
Find the gravitational force between the two spheres.
- 3
Concept
Newton's law of universal gravitation: every pair of point masses (or uniform spheres, by the shell theorem) attracts with force proportional to the product of their masses and inversely proportional to the square of their centre-to-centre distance (NCERT Class 11 Physics Chapter 7, page 130).
- 4
Formula
F = G m₁ m₂ / r²
- 5
Substitution
F = (6.674 × 10⁻¹¹) × (5.0 × 10⁴) × (3.0 × 10⁴) / (2.0)²
- 6
Calculation
Numerator: 6.674 × 10⁻¹¹ × 1.5 × 10⁹ = 6.674 × 1.5 × 10⁻² = 10.011 × 10⁻² = 1.0011 × 10⁻¹
Denominator: 4.0
F = 1.0011 × 10⁻¹ / 4.0 = 2.503 × 10⁻²
Rounding to 2 significant figures (limited by the given masses at 2 sig figs each): F ≈ 2.5 × 10⁻² N.
Note on exact values: The integer 2 in the denominator (2.0)² = 4.0 is an exact-count squaring of the given distance, which itself has 2 sig figs. G is known to 4 sig figs here. The final answer is rounded to 2 sig figs, matching the least precise given quantity. - 7
Final answer
F ≈ 2.5 × 10⁻² N (attractive, along the line joining the centres).
- 8
Common trap
Using surface-to-surface distance instead of centre-to-centre distance. If the spheres each had radius 0.5 m and the problem stated "surfaces are 1.0 m apart," the centre-to-centre distance would be 0.5 + 1.0 + 0.5 = 2.0 m, not 1.0 m. Mixing these up changes the answer by a factor of 4.
- 9
Similar NEET-style question
Two lead spheres, each of mass 6.0 × 10³ kg, have their centres 5.0 m apart. Calculate the gravitational force between them. (Answer: F = G × (6.0 × 10³)² / (5.0)² ≈ 9.6 × 10⁻⁵ N.)
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What to remember before solving Universal Law Gravitation questions
Which Universal Law Gravitation formulas do you need for NEET?
1 formula — click to collapse
Newton's law of gravitation
Attractive force between any two masses. Inverse-square central force.
| Symbol | Quantity | SI Unit |
|---|---|---|
| F | force | N |
| G | grav constant = 6.674e-11 | N*m^2/kg^2 |
| m1, m2 | masses | kg |
| r | centre-to-centre distance | m |
Valid when
- Point masses or spherically symmetric distributions
- r > sum of body radii (else use shell theorem)
More in Gravitation: 4 exam traps and mistakes · 7 formulas · 4 question patterns from its other lessons.
Universal Law Gravitation questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
Sources
NCERT refs: Class 11 Physics Chapter 7, p.130
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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