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(C) The total gravitational potential $V$ at a point $P$ inside the shell is the sum of the potential due to the particle at the centre and the potent

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$\frac{-3GM}{a}$

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(C) The total gravitational potential $V$ at a point $P$ inside the shell is the sum of the potential due to the particle at the centre and the potential due to the spherical shell.$1$. The potential due to the particle of mass $M$ at a distance $r = \frac{a}{2}$ is $V_{particle} = \frac{-GM}{r} = \frac{-GM}{a/2} = \frac{-2GM}{a}$.$2$. The potential due to a spherical shell of mass $M$ and radius $a$ at any point inside it is constant and equal to the potential at its surface,which is $V_{shell} = \frac{-GM}{a}$.$3$. The total potential at point $P$ is $V = V_{particle} + V_{shell} = \frac{-2GM}{a} + \frac{-GM}{a} = \frac{-3GM}{a}$.

$A$ particle of mass $M$ is situated at the centre of a spherical shell of mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:

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