The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. V_P and V_E are escape velocities of the planet and the earth, respectively, then

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, . . . , respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

If $${v_e}$$ is escape velocity and $${v_o}$$ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by