What will be the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth ?

Explanation

Let M be the mass of the earth. Then gravitational potential energy of the object of mass m at the surface of the earth,
`U_i=-(GMm)/R`
and the potential energy of the object , when taken to a height equal to R,
`U_f=-(GMm)/(R+R)=-(GMm)/(2R)`
`therefore` Potential energy gain `=U_f-U_i`
`=-(GMm)/(2R)-((-GMm)/R)=(GMm)/(2R)`