JEE Physics Practice Question

A thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_{0}$. A hole with a small area $\alpha 4 \pi R^{2}(\alpha \ll 1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

1. A.The potential at the center of the shell is reduced by $2 \alpha V_{0}$
2. B.The magnitude of electric field at the center of the shell is reduced by $\frac{\alpha V_{0}}{2 R}$
3. C.The ratio of the potential at the center of the shell to that of the point at $\frac{1}{2} R$ from center towards the hole will be $\frac{1-\alpha}{1-2 \alpha}$
4. D.The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance $2 R$ from the center of the spherical shell will be reduced by $\frac{\alpha V_{0}}{2 R}$