Question

The change in potential energy when a body of mass $ m $ is raised to a height $ nR $ from earths surface is (R = radius of the earth)

• A. $ mgR=\frac{n}{(n-1)} $
• B. $ mgR $
• C. $ mgR=\frac{n}{(n+1)} $
• D. $ mgR=\frac{{{n}^{2}}}{({{n}^{2}}+1)} $

Answer 1

The Correct Option is C

Change in potential energy
$ \Delta U={{U}_{2}}-{{U}_{1}} $
$ \therefore $ $ \Delta U=-\frac{GMm}{(R+nR)}+\frac{GMm}{R} $
Or $ \Delta U=-\frac{GMm}{R(1+n)}+\frac{GMm}{R} $
Or $ \Delta U=\frac{GMm}{R}\left[ -\frac{1}{1+n}+1 \right] $
Or $ \Delta U=\frac{({{R}^{2}}g)m}{R}\times \frac{n}{(1+n)} $
$ \left[ \because g=\frac{GM}{{{R}^{2}}} \right] $
Or $ \Delta U=mgR\left( \frac{n}{n+1} \right) $