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?
Practice 2easy
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?
If the distance between two masses is halved, by what factor does the gravitational force between them increase?
Practice 4easy
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?
Practice 5easy
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?
Practice 6medium
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?
Practice 7medium
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?
Practice 8medium
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:
Practice 9medium
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)
Practice 10medium
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:
Practice 11medium
If the distance between two masses is doubled, the gravitational force between them becomes:
Practice 12medium
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:
Practice 13medium
The gravitational potential at a point due to a mass M at distance r is given by:
Practice 14medium
The gravitational field intensity (gravitational acceleration) at a distance r from a point mass M is:
Practice 15hard
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)
Practice 16hard
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?
Practice 17hard
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?
Practice 18hard
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)