Question

The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is (here.R is the radius of the earth)

(a) (n/(n + 1))mgR

(b) (n/(n - 1))mgR

(c) nmgR

(d) mgR/n

Answer 1

Option (a) is correct

Explanation

Potential energy at the surface ie at a distance R from the center of the earth

E1 =-GMm/R

Potential energy at height nR ie at a distance (n+1)R from center of the earth

E2= -GMm/((n+1)R)

So the change in PE

=E2-E1= GMm/R[1-1/(n+1)]

=mgR^2/R×n/(n+1)).  (taking GM=gR^2)

=mgRn/(n+1))

=n/(n+1)×mgR

Answer 2

Correct option (a) (n/(n + 1))mgR

Explanation :

Gravitational potential energy of mass m at any point at a distance r from the centre of earth is

At the height h = nR from the surface of earth

Change in gravitational potential energy is