What is the minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ to an altitude of $2R$?

Three solid spheres each of mass $1 \ kg$ and radius $2 \ m$ are arranged at the three corners of an equilateral triangle of side $10 \ m$,such that the centers of the spheres coincide with the corners of the triangle. When they are released from that position,the speed of any one sphere at the time of collision would be ($G$ is the universal gravitational constant).

$A$ body is projected vertically upwards from the earth's surface. If its kinetic energy of projection is equal to half of its minimum value required to escape from the gravitational influence,then the height up to which it rises is ($R =$ radius of the earth).

An object of mass $m$ is raised from the surface of the earth to a height equal to the radius of the earth,that is,taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy?

The work done to raise a mass $m$ from the surface of the earth to a height $h$,which is equal to the radius of the earth,is

$A$ body starts from rest from a point at a distance $R_0$ from the centre of the Earth. The velocity acquired by the body when it reaches the surface of the Earth will be ($R$ represents the radius of the Earth).