Gravitation - Result Question 30
31. A particle of mass $M$ is situated at the centre of spherical shell of mass $M$ and radius $a$. The magnitude of the gravitational potential at a point situated at $a / 2$ distance from the centre, will be
[2011M]
(a) $\frac{2 GM}{a}$
(b) $\frac{3 GM}{a}$
(c) $\frac{4 GM}{a}$
(d) $\frac{GM}{a}$
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Answer:
Correct Answer: 31. (b)
Solution:
(b) $V_P=V _{\text{spherical shell }}+V _{\text{particle }}$
$ =\frac{G M}{a}+\frac{G M}{a / 2}=\frac{3 G M}{a} $
At every point, inside a spherical shell of radius $R$, the gravitational potential is same as that on that surface of the shell, i.e.,
$ V=-\frac{G M}{R} $
