Show that the velocity of a body released at distance r from the centre of the earth, when it strikes the surface of the earth is given by
, `v=sqrt(2GM(1/R-1/r))`where
R and M are the radius and mass of the earth. Also show that the velocity with which meteorites strike the earth's surface is equal to escape velocity.

Where is the escape velocity of a body greater -from the earth or from the moon ?

How does the escape velocity of a body from the earth depend on the mass of the body thrown ?

The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = earth's radius )

Show that the gravitational potential at a point, distance r from the mass M is given by V =-(GM/r)

An artificial satellite is moving in an orbit around the earth with a velocity equal to one-third the escape velocity from the surface of the earth. (ii) The satellite comes to rest in its orbit and then is allowed to fall freely on to the surface of the earth. Find the speed with which the satellite strikes the earth's surface. Given radius of earth =6400 km.

Time period of a simple pendulum on the surface of the earth is T_(1) and at a hight R above the surface of the earth is T_(2) , here R is the radius of the earth. The ratio T_(2)//T_(1) is