What happens to the gravitational potential at the centre of the uniform spherical shell which shrinks gradually?

The correct option is Decreases.

To understand why the gravitational potential at the centre of a uniform spherical shell decreases as it shrinks, let us look at the formula for gravitational potential.

The gravitational potential $V$ at any point inside a uniform spherical shell of mass $M$ and radius $R$ (including its centre) is constant and is given by the formula:
$V=-\frac{GM}{R}$
where $G$ is the universal gravitational constant.

Now, let us analyze what happens when the shell shrinks gradually:
1. The mass $M$ of the shell remains constant.
2. The radius $R$ of the shell decreases ($R\to \text{smaller}$).
3. As $R$ decreases, the magnitude of the term $\frac{GM}{R}$ increases.

However, because of the negative sign in the potential formula, an increase in the magnitude $\frac{GM}{R}$ means the potential $V$ becomes more negative.
In physics, a more negative potential represents a lower (decreased) potential energy state. Therefore, the gravitational potential at the centre decreases (becomes more negative) as the shell shrinks.