Question

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

• A. Increases
• B. Decreases
• C. Remains constant
• D. Oscillates

Answer 1

The correct option is B Decreases

Gravitational potential at any point P outside the shell:
$V=-\frac{GM}{r}$
Where,
$r=$ distance of point P from centre
$M=$ Mass of shell

At, $r\le R$, where $R=$ Radius of shell
This gived us the potential at the centre
$V=-\frac{GM}{R}$

Here, $M=$ Constant

Now when the shell starts sinking, the value of $R$ is decreasing. Hence the gravitational potential decrease.