Question

A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth $\left(R_e\right)$. the inerease in potential energy will be: ( $g$ = acceleration due to gravity on the surface of Earth)

• A. $\frac{1}{2}mg{R}_e$
• B. $3mg{R}_e$
• C. $\frac{2}{3}mg{R}_e$
• D. $\frac{1}{3}mg{R}_e$

Answer 1

Answer: (C)

$U=\frac{-G{M}_{e}m}{r}$
$U_i=\frac{-G{M}_{e}m}{R_e}$
$U_f=\frac{-G{M}_{e}m}{\left(R_e+h\right)}=\frac{-G{M}_{e}m}{R_e+2R_e}$
$\frac{-G{M}_{e}m}{3R_e}$
Increase in internal energy $\Delta U=U_f-U_i$
$=\frac{2}{3}\frac{G{M}_{e}m}{R_e}$
$\frac{2}{3}\frac{G{M}_e}{R_e^2}m{R}_e$
$=\frac{2}{3}mg{R}_e$