91Ó°ÊÓ

The gravitational potential at the center of a uniform spherical shell is given by \[V = -\frac{GM}{R}\] where \(V\) is the gravitational potential, \(G\) is the gravitational constant, \(M\) is the mass of the shell, and \(R\) is the radius of the shell.

As the spherical shell shrinks while maintaining its shape, its volume will decrease, and hence the radius \(R\) will also decrease. However, since it is a uniform shell, the mass \(M\) remains the same.

Let's analyze the gravitational potential formula to understand how it is affected due to the decrease in radius \(R\). The formula is: \[V = -\frac{GM}{R}\] Since \(G\) and \(M\) are constants and are not changing, we can analyze the formula based on the change in radius \(R\). We have a negative sign and the radius \(R\) in the denominator. As the radius \(R\) decreases, the fraction \(\frac{GM}{R}\) will become bigger (more negative), leading to an increase in the gravitational potential's magnitude (more negative) at the center of the shell. Therefore, as the uniform spherical shell shrinks while maintaining its shape, the gravitational potential at the center: (A) Increases (in its magnitude, since it becomes more negative)