Question 1

The gravitational potential at a point is defined as the work done per unit mass by an external agent to bring a test mass from infinity to that point. What is its SI unit?

Accepted Answer

Gravitational potential has units J/kg (energy per mass) which equals m²/s² (dimension of energy/mass).

Question 2

Two objects of masses 4 kg and 9 kg are separated by a distance of 3 m. What is the ratio of gravitational forces experienced by the two objects?

Accepted Answer

By Newton's third law, gravitational forces are equal and opposite, so the ratio is always 1:1 regardless of mass differences.

Question 3

If the distance between two masses is halved, by what factor does the gravitational force between them increase?

Accepted Answer

By Newton's law of universal gravitation, F ∝ 1/r²; reducing r to r/2 increases F by factor (2)² = 4.

Question 4

A body is taken to a height of 1600 m above Earth's surface (Earth's radius = 6400 km). By what percentage does its weight decrease?

Accepted Answer

Weight decreases by fraction 2h/R = 2(1600)/(6400000) = 0.0005 = 0.05%, approximately 0.5% for this problem scale.

Question 5

A satellite orbits Earth at a height where the gravitational acceleration is 4 m/s². If g at Earth's surface is 10 m/s², what is the ratio of orbital radius to Earth's radius?

Accepted Answer

Using g' = g(R/(R+h))², we get 4 = 10(R/(R+h))²; solving gives (R+h)/R = 2.5.

Question 6

A body is thrown vertically upward from Earth's surface with a velocity equal to the escape velocity. What is its velocity at infinite distance from Earth?

Accepted Answer

By energy conservation, if initial velocity equals escape velocity (v_e), kinetic energy at infinity is zero, so final velocity is zero.

Question 7

The escape velocity from Earth's surface is 11.2 km/s. What would be the escape velocity from a planet with twice Earth's radius and four times Earth's mass?

Accepted Answer

v_e = √(2GM/R); if M → 4M and R → 2R, then v_e' = √(2G(4M)/(2R)) = √(4GM/R) = v_e.

Question 8

Two planets have the same average density but different radii. Planet A has radius R and Planet B has radius 2R. The ratio of escape velocities from A to B is:

Accepted Answer

v_e ∝ √(MR) ∝ √(ρR³) ∝ R^(3/2); for A:B, v_eA/v_eB = (R/(2R))^(3/2) × √((2R)³/R³) = 1/2, so ratio is 1:2.

Question 9

Two identical spheres of mass 2 kg each are separated by a distance of 10 m. Calculate the gravitational force between them. (Take G = 6.67 × 10⁻¹¹ N⋅m²/kg²)

Accepted Answer

F = GM₁M₂/r² = (6.67 × 10⁻¹¹ × 2 × 2)/100 = 2.668 × 10⁻¹² N.

Question 10

Newton's law of universal gravitation states that the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to:

Accepted Answer

Newton's law states F ∝ m₁m₂/r², so force is inversely proportional to the square of distance.

Question 11

If the distance between two masses is doubled, the gravitational force between them becomes:

Accepted Answer

Since F ∝ 1/r², if r becomes 2r, then F becomes F/(2²) = F/4, i.e., one-fourth of original.

Question 12

A satellite orbits Earth at a height h above the surface where h is negligible compared to Earth's radius R. Its orbital velocity is approximately:

Accepted Answer

For a satellite close to Earth's surface, orbital velocity v = √(GM/R) since h << R.

Question 13

The gravitational potential at a point due to a mass M at distance r is given by:

Accepted Answer

Gravitational potential is defined as V = −GM/r (negative because gravity is attractive).

Question 14

The gravitational field intensity (gravitational acceleration) at a distance r from a point mass M is:

Accepted Answer

Gravitational field intensity is the force per unit mass: g = F/m = GM/r².

Question 15

A mass m is taken from the surface of Earth (radius R) to a height of 3R above the surface. How much work must be done against gravity? (Take gravitational potential energy at infinity as zero)

Accepted Answer

Work = Change in PE = U_final − U_initial = −GMm/4R − (−GMm/R) = 3GMm/4R.

Question 16

A satellite orbits Earth at a height h above the surface where h is equal to Earth's radius R. If the gravitational acceleration at Earth's surface is g, what is the acceleration due to gravity at the satellite's location?

Accepted Answer

At height h = R, the distance from Earth's centre is 2R, so g' = GM/(2R)² = g/4 (since g = GM/R²).

Question 17

A planet has twice the mass of Earth and half the radius of Earth. If the escape velocity from Earth is v_e, what is the escape velocity from this planet?

Accepted Answer

Escape velocity v = √(2GM/R); for the planet, v_p = √(2G(2M)/(R/2)) = √(8GM/R) = 2√(2GM/R) = 2v_e.

Question 18

Two identical spheres of mass M are separated by a distance of 2 m. If the gravitational force between them is 6.67 × 10⁻¹¹ N, find the mass M of each sphere. (Use G = 6.67 × 10⁻¹¹ N·m²/kg²)

Accepted Answer

Using F = GM²/r², we get 6.67 × 10⁻¹¹ = (6.67 × 10⁻¹¹ × M²)/4, solving gives M = 2 kg.

Agniveer Army Technical Gravitation

Gravitation — Practice Questions