If the acceleration due to gravity at the surface of the earth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is

Options

A. `(mgnR)/((n+1))`
B. `(mg(n+1)R)/(n)`
C. `(mgR)/((n+1))`
D. none of these

Answer

a

Explanation

`PE_(2)-PE_(1)=-(GMm)/(R+nR)+(GMm)/(R)`
`=(GMm)/(R)[1-(1)/(n+1)]`
`=(GMm)/(R)[(n+1-1)/(n+1)]`
`=(gR^(2)m)/(R)(n)/(n+1)`
`=("mg Rn")/(n+1)`