A mass ' ( m ) ' on the surface of the Earth is shifted to a target equal to the radius of the Earth. If ' ( R ) ' is the radius and ' ( M ) ' is the mass of the Earth, then work done in this process is

Step-by-step solution

Gravitational potential energy on surface on Earth is [ U_ E = -G M m R ] where ( M ) is mass of Earth; ( m ) is mass on surface of Earth; ( R ) is radius; ( G ) is gravitational constant When mass ( m ) is shifted to a target then potential energy is [ U= -G M m (R+R) = -G M m 2 R ] Work done in the process is [ array l W=U-U_ E =- G M m 2 R - (- G M m R )=- G M m 2 R + G M m R W= G M m 2 R array ] Now substitute ( G M=g R² ), we get [ W= g R² m 2 R = g R m 2 ] Therefore, work done in process ( = m g R 2 )