A body of mass m is placed on the earth's surface. It is taken from the earth's surface to a height h=3 R,(R is radius of earth ) . The change in gravitational potential energy of the body is

Step-by-step solution

Gravitational potential energy on the surface of earth, U₁=- G M m R where, M= mass of earth. and R= radius of earth. Gravitational potential energy at height h=3 R is given as aligned U₂ & =- G M m R+h =- G M m R+3 R U₂ & =- G M m 4 R aligned Change in gravitational potential energy, U=U₂-U₁=- G M m 4 R - (- G M m R ) [from Eqs. (i) and (ii)] aligned & =- G M m 4 R + G M m R = 3 4 G M m R & = 3 4 g R^2 m R [ G M=g R^2 ] & = 3 4 m g R aligned