A body of mass 2 m is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of h , where h=4 R .

Step-by-step solution

Potential energy, U=- G M m r = -2 G M m r [ m=2 m] At earth's surface, r=R U_e=- 2 G M m R Now, if a body is taken to height, h=4 R , then the potential energy is given by aligned U_h & =- 2 G M m R+h [ r=h+R] & = -2 G M m 5 R aligned Thus, change in gravitational potential energy, aligned U & =U_h-U_e & =- 2 G M m 5 R + 2 G M m R = 8 5 G M m R aligned aligned U & = 8 5 g R^2 m R [ G M=g R^2 ] & = 8 5 m g R aligned