Gravitation Ques 25
25. Infinite number of bodies, each of mass $2 $ $kg$ are situated on $x$-axis at distances $1 $ $m, 2 $ $m, 4 $ $m$, $8$ $ m, \ldots .$. respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
[2013]
(a) $-\frac{8}{3} G$
(b) $-\frac{4}{3} G$
(c) $-4 G$
(d) $- G$
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Answer:
Correct Answer: 25.(c)
Solution:
- (c)
Gravitational potential $V=\frac{-Gm}{r}$
$V_0=-\frac{G \times 2}{1}-\frac{G \times 2}{2}-\frac{G \times 2}{4}-\frac{G \times 2}{8}\ldots \infty$
$V_0=-2 G[1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots \infty]$
$V_0=-2 G \times \frac{1}{(1-\frac{1}{2})}=-2 G \times \frac{1}{\frac{1}{2}}=-4$ $ G$.
BETA
