The change in potential energy when a body of mass m is raised to a height nr from the earth surface is
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Answer:
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
hope it helps
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