The uniform spherical shell is shown in the figure below
Inside the shell, there is no mass, so by applying Gauss’s law forgravitation
∮g.da=−4πGMenclosed where, g = gravitational field intensity.
da = area enclosed
G = gravitational constant
and
Menclosed= mass enclosed .
As,
Menclosed=0 So, gravitational field intensity is zero inside the shell, i.e. g = 0 …(i)
We also know that,
g=− where, dV is change in potential due to gravity
⇒ V = constant [using Eq. (i)]
So, gravitational field is zero everywhere inside the shell and
gravitational potential (V) is constant everywhere.