Gravitation Ques 31
31. Assuming the radius of the earth as $R$, the change in gravitational potential energy of a body of mass $m$, when it is taken from the earth’s surface to a height $3 R$ above its surface, is
[2002]
(a) $3 $ $m g R$
(b) $\frac{3}{4} $ $m g R$
(c) $1$ $ mg R$
(d) $\frac{3}{2}$ $ m g R$
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Answer:
Correct Answer: 31.(b)
Solution:
- (b) Gravitational potential energy $(GPE)$ on the surface of earth,
$E_1=-\frac{G M m}{R}$
$GPE$ at $3 R, E_2=-\frac{G M m}{(R+3 R)}=-\frac{G M m}{4 R}$
$\therefore$ Change in $GPE$
$=E_2-E_1=-\frac{G M m}{4 R}+\frac{G M m}{R}=\frac{3 G M m}{4 R}$
$=\frac{3 g R^{2} m}{4 R} \quad(\because g=\frac{G M}{R^{2}})$
$=\frac{3}{4}$ $m g R$
BETA
