Question

If a body of mass $m$ is sent to a height of $R/5$ from the earth surface, the potential energy increases by $(R\to$ radius of earth):-

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

Answer 1

The correct option is A $\frac{mgR}{6}$

Gravitational potential energy at earth surface
$U_i=-\frac{GMm}{R}...\left(i\right)$

Gravitional potential energy at height
$(h=\frac{R}{5})$
$U_f=-\frac{GMm}{R+\frac{R}{5}}...\left(ii\right)$

Increases in potential energy:
$\left(\Delta U\right)=U_f-U_i$

$\Delta U=-\frac{5}{6}\frac{GMm}{R}-(-\frac{GMm}{R})$

$\Delta U=\frac{1}{6}\frac{GMm}{R}$

As $g=$ acceleration due to gravity, $g=\frac{GM}{R^2}$

$\Delta U=\frac{1}{6}\frac{g{R}^{2}m}{R}$

$\Delta U=\frac{mgR}{6}$