Q66 / 90 · JEE Main 2023 (11 Apr Shift 2) · Physics

If $V$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

A
$\frac{4}{3} V$
B
$\frac{V}{2}$
C
$V$
Correct answer
D
$\frac{3 V}{2}$

Solution

The magnitude of gravitational potential of a solid sphere at a distance $r$ from the centre is
$V = \frac{- G M}{2 R^{3}} (3 R^{2} - r^{2})$
At $r = R$ , $V = \frac{- G M}{R}$ .
At $r = 0$ , $V' = \frac{- G M}{2 R^{3}} (3 R^{2}) = \frac{- 3 G M}{2 R}$
Clearly, $V' = \frac{3 V}{2}$ .

Hence, the correct answer is option: 'D'.

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If V is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

Solution

Relevant Questions

If $V$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be: