Question

Assertion: The magnitude of the gravitational potential at the surface of a solid sphere is less than that of the center of the sphere.
Reason: Due to the solid sphere, the gravitational potential is the same within the sphere.

Answer 1

Hint: As we all know that due to the virtue of the position of the body, an object possesses an energy and that energy is called gravitational potential energy. It is the energy possessed by the object in a conservative field.

Complete Step-by-step Solution
Consider two spheres one is Earth, and another one is Jupiter with radii R and R’. In the given question, We have seen that this gravitational potential energy is more useful near the close surface of the earth where the value of acceleration is $9.8\;m/{s^2}$.
Here, we will use the gravitational potential formula for a sphere.
\[V = - \dfrac{{GM}}{{2{R^3}}}[3{R^2} - {r^2}]\].
Here V is the gravitational potential energy, R is the radius of the sphere, $G$ is the gravitational constant of the sphere, and M is the mass of the sphere and r is the distance from the center of the sphere to any arbitrary point.
We can see that the magnitude of gravitational potential is varying with the distance of the observation point. On the surface of sphere \[r = R\] and center of sphere \[r = 0\]
Given: The magnitude of gravitational potential $V$ at the surface of a solid sphere is less than that of the center of the sphere. The gravitational potential can be represented by the below formula used.
\[V = - \dfrac{{GM}}{{2{R^3}}}[3{R^2} - {r^2}]\].
Let point P on the surface of the solid sphere the \[r = R\]. So, equation can be written as,
\[V = - \dfrac{{GM}}{{2{R^3}}}[3{R^2} - {r^2}]\]
\[ \Rightarrow {V_{{\rm{surface}}}} = - \dfrac{{GM}}{R}\]
Let us assume that a point $P$ in the center of a solid sphere then \[r = 0\]. So, the equation can be written as,
\[ \Rightarrow {V_{{\rm{Center}}}} = - 1.5\dfrac{{GM}}{R}\]
\[\therefore \left| {{V_{{\rm{Surface}}}}} \right| < \left| {{V_{{\rm{Center}}}}} \right|\]

So, the assertion is correct but the reason is false.

Note:
So here we can conclude that the magnitude of gravitational potential is depending on the distance from the center. If the observation point is increasing above the surface of the sphere with respect to the center of the sphere, then the potential will decrease and If the observation point is decreasing from the surface of the sphere with respect to the center of the sphere then the potential will increase.