Question

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

• A. $mgh$
• B. $\frac{5}{6}mgh$
• C. $\frac{3}{5}mgh$
• D. $\frac{6}{7}mgh$

Answer 1

The correct option is B $\frac{5}{6}mgh$

The gravitational potential energyt is given by:

$GPE=-\frac{GMm}{r}$

Increase on gravitational potential energy is :

$\Delta E=PEatheight-PEatground$

$[-\frac{GMm}{R+\frac{R}{5}}]-[-\frac{GMm}{R}]=\frac{GMm}{R}-\frac{GMm\times 5}{6R}$

$=\frac{GMm}{R}[1-\frac{5}{6}]=\frac{GMm}{R}\times \frac{1}{6}$

$=\frac{mg{R}^2}{6R}=\frac{1}{6}mgR=\frac{5}{6}mgh[\because R=5h]$