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A body of mass M is placed at the centre of a uniform spherical shell of equal mass and radius ‘a’. The gravitational potential at a point ‘p’ at a distance $\frac{a}{2}$ from the centre is

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- \frac{3GM}{a}

\frac{2GM}{a}

\frac{4GM}{a}

answer is A.

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Detailed Solution

Gravitational potential at the point P due to the particle at the centre is

$V_{1} = - \frac{GM}{R} = - \frac{2GM}{a} R = a/2$

Gravitational potential at ‘p’ due to spherical shall is $V_{2} = - \frac{GM}{a}$

$V = V_{1} + V_{2}$

$= - \frac{2GM}{a} - \frac{GM}{a} = - \frac{3GM}{a}$

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