Question

A body of mass $2m$ is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of $h$, when $h=4R$.

• A. $\frac{2mgh}{R}$
• B. $\frac{2}{3}mgR$
• C. $\frac{8}{5}mgR$
• D. $\frac{mgR}{2}$

Answer 1

The correct option is C $\frac{8}{5}mgR$

Potential energy, $U=-\frac{GMm}{r}=\frac{-2GMm}{r}$ $[\because m=2m]$
At earth's surface, $r=P$
$\therefore U_e=-\frac{2GMm}{R}$
Now, if a body is taken to height, $h=4R$, then the potential energy is given by
$U_h=-\frac{2GMm}{R+h}$ $[\because r=h+R]$
$=\frac{-2GMm}{5R}$
Thus, change in gravitational potential energy.
$\Delta U=U_h-U_e$
$=-\frac{2GMm}{5R}+\frac{2GMm}{R}=\frac{8}{5}\frac{GMm}{R}$
$\therefore \Delta U=\frac{8}{5}\frac{g{R}^{2}m}{R}$ $[\because GM=g{R}^2]$
$=\frac{8}{5}mgR$