An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g = 10 m s - 2 and radius of earth = 6400 km ]

Step-by-step solution

Gravitational potential energy on the earth surface U i = - G M m R Gravitational potential energy at a height h above the earth's surface U f = - G M m R + h = - G M m R + 3 R = - G M m 4 R Gain in gravitational potential energy Δ U = U f - U i = - G M m 4 R + G M m R = G M m + 4 G M m 4 R =   3 G M m 4 R Gravitational potential energy in terms of acceleration due to gravity is ∆ U = 3 4 m g R = 3 4 × 1 × 10 × 64 × 10 5 = 48   MJ