Question

what is the gain in potential energy of an object of mass m raised from the surface of earth to a height R (Acceleration due to gravity at the surface of earth = g, radius of earth = R)

Answer 1

Answer:

1/2 mgR

Explanation:    

Gravitational potential energy on the earth surface, Ur =  −GMm/R

​ Gravitational potential energy at a height h above the earth's surface, Uh

​=  −GMm/R+h

​ Uh  = −GMm/R+R   = −GMm/2R

Gain in gravitational potential energy = Uh − Ur =

−GMm/2R  −( −GMm/R) = GMm/R - GMm/2R

= 1/2 mgR

  Hope it helps....