Question

A body of mass $m$ rises to a height $h=\frac{R}{5}$ from the earth's surface where $R$ is earth's radius. If $g$ is acceleration due to gravity at the earth's surface, the increase in potential energy will be

• A. $mgh$
• B. $\frac{4}{5}mgh$
• C. $\frac{5}{6}mgh$
• D. $\frac{6}{7} mgh$

Answer 1

Answer: (C)

$\frac{5}{6}mgh$

Answer 2

Increase in gravitational potential energy $=\left[-\frac{G M m}{h+ R}\right]-\left[-\frac{G M m}{R}\right]$ $=\left[-\frac{G M m}{R+\frac{R}{5}}\right]-\left[-\frac{G M m}{R}\right]$ $\left[\because h=\frac{R}{5}\right]$ $=\frac{G M m}{R}-\frac{G M m \times 5}{6 R}$ $=\frac{G M m}{R}\left[1-\frac{5}{6}\right]=\frac{G M m}{R} \times \frac{1}{6}$ $=\frac{m g R^{2}}{6 R}=\frac{1}{6} m g R=\frac{5}{6} m g h$ $[\because R=5 h]$