Work done in raising a body of mass m from the surface of the earth to a height R 3 is ......... (where, R is radius of earth, M is mass of the earth and G is gravitational constant)

Step-by-step solution

At surface, gravitational potential energy, U₁= -G M m R At height n R, U₂= -G M m R+n R aligned |U₂-U₁ | & = | ( -G M m R+n R )- ( -G M m R ) | & = G M m R - G M m R+n R & = G M m R (1- 1 n+1 )= ( n n+1 ) G M m R aligned For height x= R 3 , n= 1 3 Work done = |U₂-U₁ |= ( 1 3 1 3 +1 ) G M m R = G M m 4 R