Q131 / 160 · TS EAMCET 2023 (14 May Shift 2) · Physics

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
    $\mathrm{mg} / \mathrm{h}$
  • Correct answer
    B
    $\frac{5}{6} \mathrm{mgh}$
  • C
    $\quad \frac{3}{5} \mathrm{mgh}$
  • D
    $\frac{6}{7} \mathrm{mgh}$

Solution

Given $\mathrm{h}=\frac{\mathrm{R}}{5}$ Potential Energy at surface of the earth, $\left(\mathrm{PE}_1\right)=-\frac{\mathrm{GMm}}{\mathrm{R}}$ Potential Energy at height $h=\frac{R}{5},\left(P_2\right)=-\frac{G M m}{R+\frac{R}{5}}=-\frac{5 G M m}{6 R}$ Increase in Potential energy $=\mathrm{PE}_2-\mathrm{PE}_1=-\frac{5 \mathrm{GMm}}{6 \mathrm{R}}+\frac{\mathrm{GMm}}{\mathrm{R}}=\frac{\mathrm{GMm}}{6 \mathrm{R}}$ (Using $g=\frac{G M}{R^2}$ and $h=\frac{R}{5}$ ) $\Rightarrow P_2-P_1=\frac{5}{6} \mathrm{mgh}$

Hence, the correct answer is option: 'B'.

Relevant Questions