A body of mass $m$ is placed on Earth's surface which is a taken from Earth's surface to a height of $h=3 R$…

A body of mass $m$ is placed on Earth's surface which is a taken from Earth's surface to a height of $h=3 R$, then the change in the gravitational potential energy is:
  1. $\frac{m g R}{4}$
  2. $\frac{2}{3} m g R$
  3. $\frac{3}{4} m g R$
  4. $\frac{m g R}{2}$

Solution

$\begin{aligned} & \therefore \text { change in GPE }=\text { final } \\ & \text { energy }- \text { initial energy } \\ & =-\frac{G M m}{4 R}+\frac{\mathrm{GMm}}{R} \\ & =-\frac{G M m}{4 R}\left[1-\frac{1}{4}\right]=\frac{3}{4} \frac{G M m}{4 R} \\ & =\frac{3}{4} \frac{G M}{R^2} m R=\frac{3}{4} g m R \end{aligned}$ .

Asked in: NEET 2002

Practice more Gravitation questions on Aicharya