Gravitation Physics - Gravitation

Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?

The radius of a planet is R₁ and a satellite revolves round it in a circle of radius R₂. The time period of revolution is T. Find the acceleration due to the gravitation of the planet at its surface.

A Mars satellite moving in an orbit of radius 9.4 × 10³km takes 27540s to complete one revolution. Calculate the mass of Mars.

Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?

Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.

The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 x 10⁵km. Calculate the mass of the earth from these data.

Two small bodies of masses 10kg and 20kg are kept a distance 1.0m apart and released, Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to 0.5m.

Find the acceleration due to gravity of the moon at a point 1000km above the moon's surface. The mass of the moon is 7.4 × 10²²kg and its radius is 1740km.

No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?

Let V and E represent the gravitational potential and field at a distance r from the centre of a uniform solid sphere. Consider the two statements:

1. The plot of V against r is discontinuous.
2. The plot of E against r is discontinuous.

1. Both A and B are correct.
2. A is correct but B is wrong.
3. B is correct but A is wrong.
4. Both A and B are wrong.

Inside a uniform spherical shell:

1. The gravitational potential is zero.
2. The gravitational field is zero.
3. The gravitational potential is same everywhere.
4. The gravitational field is same everywhere.

A body is suspended from a spring balance kept in a satellite. The reading of the balance is W₁ when the satellite goes in an orbit of radius R and is W₂ when it goes in an orbit of radius 2R.

1. W₁ = W₂
2. W₁ < W₂
3. W₁ > W₂
4. W₁ ≠ W₂

The magnitude of gravitational potential energy of the moon-earth system is U with zero potential energy at infinite separation. The kinetic energy of the moon with respect to the earth is K.

1. U < K
2. U > K
3. U = K

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre:

1. Increases.
2. Decreases.
3. Remains constant.
4. Oscillates.

Three equal masses m are placed at the three corners of an equilateral triangle of side a. Find the force exerted by this system on another particle of mass m placed at,

1. The mid-point of a side,
2. At the centre of the triangle.

Four particles having masses m, 2m, 3m and 4m are placed at the four corners of a square of edge a. Find the gravitational force acting on a particle of mass m placed at the centre.

A satellite of mass 1000kg is supposed to orbit the earth at a height of 2000km above the earth's surface. Find

1. Its speed in the orbit.
2. Its kinetic energy.
3. The potential energy of the earth-satellite system.
4. Its time period. Mass of the earth = 6 × 10²⁴kg.