Gravitational potential at the centre of a uniform solid sphere of mass ‘M’ and radius ‘R’ is (if potential due to the sphere at the infinity is $\frac{GM}{R}$ .)

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$- \frac{GM}{R}$

$- \frac{GM}{2 R}$

$- \frac{3 GM}{2 R}$

None

answer is B.

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Detailed Solution

Two gravitational potential at infinity is $\frac{GM}{R}$ . Hence everywhere potential will be increased by $\frac{GM}{R}$ . So potential at the centre is $\frac{- 3 GM}{2 R} + \frac{GM}{R} = \frac{- GM}{2 R}$ .

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