If is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

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Solution

Q.
If $V$ is the gravitational potential due to a sphere of uniform density on its surface, then its value at the center of the sphere will be [2023]

1 $\frac{3 V}{2}$

2 $V$

3 $\frac{4}{3} V$

4 $\frac{V}{2}$

Ans.
(1)

$V = \frac{G M}{2 R^{3}} (3 R^{2} - r^{2}) at r = R \Rightarrow V = (\frac{G M}{R})$

$At r = 0, V_{0} = \frac{3 G M}{2 R} = (\frac{3 V}{2})$

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