Question

A body of mass $m$ is taken from surface of earth to height of $5R$. If gravity at surface is $g_o$, then work done by external force to move the body is (neglect air resistance)

• A. $5m{g}_{0}R$
• B. $\frac{m{g}_{0}R}{6}$
• C. $\frac{5m{g}_{0}R}{4}$
• D. $\frac{5m{g}_{0}R}{6}$

Answer 1

The correct option is D $\frac{5m{g}_{0}R}{6}$

$W=\Delta U=U_f-U_i$
$=-\frac{GMm}{6R}+\frac{GMm}{R}=\frac{GMm}{R}\{1-\frac{1}{6}\}$
$=\frac{5GMm}{6R}=\frac{5}{6}\frac{GM}{R^2}mR$
$=\frac{5}{6}m{g}_{0}R$