A mass m is raised from the surface of earth to a point which is at a height nR from the surface of earth. Change in potential energy is :

Options

A. nmgR
B. `(2mgR)/(h)`
C. `(n)/(n+1)` (mgR)
D. `(mgR)/(n)`

Answer

C

Explanation

Change in p.E `=(-GMm)/(R+nR)-((-GMm)/(R ))`
`=(GMm)/(R )-(GMm)/(R(n+1))=(GMm)/(R ) [1-(1)/(n+1)]`
`=(GMm)/(R )[(n+1-1)/(n+1)]=(gR^(2)m)/(R )[(n)/(n+1)]`
`=(n)/(n+1)mgR`
So the correct choice is (c ).