Question

A hollow spherical shell is compressed to half of its radius, the gravitational potential at the centre.

• A. decreases
• B. increases
• C. remains same
• D. During the compression increases and then returns at the previous value.

Answer 1

The correct option is A decreases

Gravitational potential of a spherical shell at a point inside is given by
$$V_p=-\frac{GM}{R}$$ As the shell is compressed to half its radius the mass will still remain same.
The new potential will be

$V_p^{\prime }=-\frac{GM}{\left(\frac{R}{2}\right)}=-\frac{2GM}{R}$

Thus, due to the negative sign, when the radius is halved the potential decreases.

Hence, option (b) is the correct answer.

Key Concept: The gravitational potential at inside a spherical shell is given by, $V=-\frac{GM}{R}$ and is a constant