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qUESTIONS

A projectile is projected with velocity kve in vertically upward direction from the ground into the space. (ve is escape velocity and k < 1 ) . If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be: (R = radius of earth)

A small asteroid is orbiting around the sun in a circular orbit of radius r0 with speed V0. A rocket is launched from the asteroid with speed V = αV0 where V is the speed relative to the sun. The highest value of α for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effect of other planets)

The time period of a simple pendulum on a freely moving artificial satellite is

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is

Two spheres of mass m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

The height at which the weight of a body becomes 1/16th, its weight on the surface of earth (radius R), is

If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that of the earth, the gravitational acceleration on the surface of that planet is

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

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