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JEE Main Gravitation — practice questions

Explore 64 free Gravitation questions in JEE Main Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Gravitation: quick revision

For a spherical mass outside its surface, measure r from the centre. Gravity follows an inverse-square law. A circular orbit uses gravity as its centripetal force; escape speed follows from an energy balance with zero potential energy at infinity.

Key ideas and when to use them

  • $F=GMm/r^2$, and $g=GM/r^2$.
  • Circular-orbit speed: $v=\sqrt{GM/r}$.
  • Escape speed from radius R: $v_e=\sqrt{2GM/R}=\sqrt{2gR}$.

Common mistakes

  • Height above the surface is not the same as distance from the centre.
  • An orbiting object can have zero apparent weight while gravity still acts.

Three worked examples

Example 1: Two masses exert 16 N on each other. What is the force when their separation doubles?
  1. Keep the masses fixed.
  2. Inverse-square scaling gives $F_2=16/2^2$.

4 N

Example 2: A circular orbit has GM/r = 16 × 10⁶ m²/s². Find the orbital speed.
  1. For a circular orbit, $v^2=GM/r$.
  2. $v=\sqrt{16\times10^6}$.

4000 m/s

Example 3: A spherical body has surface g = 8 m/s² and radius 10⁶ m. Find its surface escape speed, ignoring air.
  1. Use $v_e=\sqrt{2gR}$.
  2. $v_e=\sqrt{2\times8\times10^6}$.

4000 m/s

Qallery AI-assisted study notes and original examples. Further reading: NCERT Physics — Gravitation.

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Gravitation questions and exercises with answers

Showing questions 1–30 of 64.

As per your syllabus, Kepler's law of areas states which quantity is constant for a planetary orbit?Read the answer and worked solution →As per your syllabus, Kepler's law of periods states which relation between period T and semi-major axis a?Read the answer and worked solution →As per your syllabus, Kepler's 2nd law (equal areas in equal times) is equivalent to conservation of which quantity?Read the answer and worked solution →As per your syllabus, Newton's UNIVERSAL law of gravitation states that F between two point masses is proportional to which?Read the answer and worked solution →As per your syllabus, the value of the universal gravitational constant G is approximately which?Read the answer and worked solution →As per your syllabus, the FIRST experimental measurement of G was made by which scientist and when?Read the answer and worked solution →As per your syllabus, the force on mass m₂ due to m₁ and the force on m₁ due to m₂ obey which relation?Read the answer and worked solution →As per your syllabus, the gravitational force between two point masses is which type of force in nature?Read the answer and worked solution →As per your syllabus, the dimensions of the gravitational constant G are which?Read the answer and worked solution →As per your syllabus, Table 7.1, Kepler's 3rd law is verified by planetary data showing T² / a³ is which?Read the answer and worked solution →As per your syllabus, eqn 7.12, the acceleration due to gravity on Earth's surface is given by which expression?Read the answer and worked solution →As per your syllabus, eqn 7.15, for SMALL height h (h ≪ R_E) above Earth, the variation of g with h is approximately which?Read the answer and worked solution →As per your syllabus, eqn 7.19, for depth d BELOW Earth's surface, the variation of g with d is which?Read the answer and worked solution →As per your syllabus, the value of g is MAXIMUM at which location on or near the Earth?Read the answer and worked solution →As per your syllabus, the value of g at the CENTRE of the Earth (assuming uniform density) is which?Read the answer and worked solution →As per your syllabus, at height h equal to R_E above the surface, the value of g(h) becomes which fraction of surface g?Read the answer and worked solution →As per your syllabus, using g and R_E gives M_E ≈ which value?Read the answer and worked solution →As per your syllabus, using the Moon's orbital data (T=27.3 d, R = 3.84×10⁸ m) gives M_E ≈ which value?Read the answer and worked solution →As per your syllabus, the gravitational acceleration of a body INSIDE a uniform spherical shell of mass M is which?Read the answer and worked solution →As per your syllabus, the dimensions of g (acceleration due to gravity) are which?Read the answer and worked solution →As per your syllabus, eqn 7.15, for an altitude of h = 8 km above Earth (R_E = 6400 km), g decreases by approximately what fraction?Read the answer and worked solution →As per your syllabus, eqn 7.25, the gravitational potential energy of a particle of mass m at distance r from a mass M (V = 0 at ∞) is which?Read the answer and worked solution →As per your syllabus, the gravitational PE for two particles of masses m₁ and m₂ separated by r is which?Read the answer and worked solution →As per your syllabus, eqn 7.31, the escape speed from a planet of mass M and radius R is which expression?Read the answer and worked solution →As per your syllabus, eqn 7.32, the escape speed can also be written using g and R as which?Read the answer and worked solution →As per your syllabus, the numerical value of escape speed from the Earth's surface is approximately which?Read the answer and worked solution →As per your syllabus, the escape speed from the Moon's surface is approximately which?Read the answer and worked solution →As per your syllabus, the gravitational PE of a particle DOUBLED in distance (r → 2r) from a mass M changes from −GMm/r to which?Read the answer and worked solution →As per your syllabus, total gravitational PE of four equal masses at corners of a square of side l is approximately which?Read the answer and worked solution →As per your syllabus, the escape speed from a planet depends on which set of properties?Read the answer and worked solution →

Worked practice questions

As per your syllabus, Kepler's law of areas states which quantity is constant for a planetary orbit?

  1. Orbital radius r
  2. Angular acceleration α
  3. Linear speed v
  4. Areal velocity (dA/dt)
Show answer and solution

Correct answer: D. Areal velocity (dA/dt)

Your syllabus: the line joining Sun-planet sweeps equal areas in equal times. Equivalent to L = constant.

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As per your syllabus, Kepler's law of periods states which relation between period T and semi-major axis a?

  1. T ∝ a²
  2. T² ∝ a³
  3. T ∝ a
  4. T³ ∝ a²
Show answer and solution

Correct answer: B. T² ∝ a³

Your syllabus: T² ∝ a³. The proportionality constant equals 4π²/(GM_sun).

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As per your syllabus, Kepler's 2nd law (equal areas in equal times) is equivalent to conservation of which quantity?

  1. Mechanical energy
  2. Linear momentum
  3. Total energy
  4. Angular momentum
Show answer and solution

Correct answer: D. Angular momentum

Your syllabus: dA/dt = L/(2m) is constant since L is conserved (gravity is a central force).

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