Question

The earth's radius is R and acceleration due to gravity at its surface is g. If a body of mass m is sent to a height $h=\frac{R}{5}$ from the earth's surface, the potential energy increases by

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

Answer 1

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

Increase in potential energy
$\Delta U=U_2-U_1$
$=[-\frac{GMm}{(R+\frac{R}{5})}]-[-\frac{GMm}{R}]$
$=\frac{GMm}{R}-\frac{5GMm}{6R}$
$=\frac{GMm}{6R}=\frac{g{R}^{2}m}{6R}=\frac{mgR}{6}$
$=mg.\frac{5h}{6}=\frac{5}{6}mgh$