Gravitation Physics - Gravitation

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is νe. Its speed with respect to the satellite:

1. Will be less than ν_e.
2. Will be more than ν_e.
3. Will be equal to ν_e.
4. Will depend on the direction of projection.

The time period of an earth-satellite in circular orbit is independent of:

1. The mass of the satellite.
2. Radius of the orbit.
3. None of them.
4. Both of them.

The acceleration of the moon just before it strikes the earth in the previous question is:

1. 10ms^-2
2. 0.0027ms^-2
3. 6.4ms^-2
4. 5.0ms^-2

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.

Two satellites going in equatorial plane have almost same radii. As seen from the earth one moves from east to west and the other from west to east. Will they have the same time period as seen from the earth? If not, which one will have less time period?

Can you think of two particles which do not exert gravitational force on each other?

At noon, the sun and the earth pull the objects on the earth's surface in opposite directions. At midnight the sun and the earth pull these objects in same direction. Is the weight of an object, as measured by a spring balance on the earth's surface, more at midnight as compared to its weight at noon?

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

A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.

As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/ she not feel weightless as a satellite passenger does?

A body stretches a spring by a particular length at the earth's surface at equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.

A spacecraft consumes more fuel in going from the earth to the moon than it takes for a return trip. Comment on this statement.

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?

A particle is fired vertically upward with a speed of 15km/s. With what speed will it move in intersteller space. Assume only earth's gravitational field.

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if,

1. r < x < 2r.
2. 2r < x < 2R.
3. x > 2R.

An apple falls from a tree. An insect in the apple finds that the earth is falling towards it with an acceleration g. Who exerts the force needed to accelerate the earth with this acceleration g?

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.