Question

What is the charge in gravitational potential energy when a body of mass m is raised to a height nR from surface of earth? (R is radius of earth) ​

Answer 1

Potential energy at surface of earth will be PE1 = (G.M.m)/R

Now, potential energy at height nR from the surface of earth, PE2 = (G.M.m)/(R+nR)

Here, change in PE = PE1 – PE2

= (G.M.m)/R – (G.M.m)/(n+1)R

= (G.M.m)/R[1 – 1/(n+1)]

= (G.M.m)/R[(n + 1 – 1)/(n+1)]

= [n/(n+1)](G.M.m)/R ….(i)

Also, g = GM/(R^2) ….(ii)

From (i) and (ii),

Change in PE = (n/(n+1))mgR