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A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at a/ 2 distance from the centre, will be
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Verified Answer
The correct answer is:
$-\frac{3 G M}{a}$
Gravitational potential at point a/2 distance from centre
$$
\begin{aligned}
& =-\frac{\mathrm{GM}}{\mathrm{a}}-\frac{\mathrm{GM}}{\mathrm{a} / 2} \\
& =-\frac{3 \mathrm{GM}}{\mathrm{a}}
\end{aligned}
$$
$$
\begin{aligned}
& =-\frac{\mathrm{GM}}{\mathrm{a}}-\frac{\mathrm{GM}}{\mathrm{a} / 2} \\
& =-\frac{3 \mathrm{GM}}{\mathrm{a}}
\end{aligned}
$$
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