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A particle of mass $M$ is situated at the centre of spherical shell of mass and radius $a$. The magnitude of the gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be
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The correct answer is:
$\frac{3 G M}{a}$
$V_P=V_{\text {sphere }}+V_{\text {partical }}$
$$
\begin{aligned}
& V_P=\frac{G M}{a}+\frac{G M}{a / 2} \\
& V=\frac{G M}{a}+\frac{2 G M}{a} \\
& V_P=\frac{3 G M}{a}
\end{aligned}
$$
$$
\begin{aligned}
& V_P=\frac{G M}{a}+\frac{G M}{a / 2} \\
& V=\frac{G M}{a}+\frac{2 G M}{a} \\
& V_P=\frac{3 G M}{a}
\end{aligned}
$$
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