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

Answer: (C)

$mgR=\frac{n}{(n+1)}$

Answer 2

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 $\Delta U=mgR\left( \frac{n}{n+1} \right)$