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(C) The gravitational potential at any point on the surface of the spherical shell is the sum of the potential due to the particle at the centre and t

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$-\frac{4Gm}{R}$

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(C) The gravitational potential at any point on the surface of the spherical shell is the sum of the potential due to the particle at the centre and the potential due to the shell itself.$1$. The potential due to the particle of mass $m$ at a distance $R$ (on the surface) is $V_1 = -\frac{Gm}{R}$.$2$. The potential due to a uniform spherical shell of mass $3m$ and radius $R$ at any point on its surface is $V_2 = -\frac{G(3m)}{R}$.$3$. The total gravitational potential $V$ on the surface is $V = V_1 + V_2$.$V = -\frac{Gm}{R} + \left(-\frac{3Gm}{R}\right) = -\frac{4Gm}{R}$.

$A$ particle of mass $m$ is placed at the centre of a uniform spherical shell of mass $3m$ and radius $R$. The gravitational potential on the surface of the shell is

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