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qUESTIONS

A planet orbits in an elliptical path of eccentricity e around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by P and the point where it is farthest is denoted by A. Let Vp and VA be the respective speeds at P and A, Then

A satellite of mass m is orbiting close to the surface of the earth (Radius R = 6400 km) has a kinetic energy K. The corresponding kinetic energy of the satellite to escape from the earth’s gravitational field is

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

A spherical planet has a mass Mp and diameter Dp. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

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

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