Question

Gravitational potential on the surface of an isolated uniform solid sphere of mass and radius is found to be a spherical cavity having a radius that is created inside the sphere which is touching the surface of the original sphere. The cavity is then filled with material having density 16 times that of the original sphere. The options are:

Options:
a. The gravitational potential remains unchanged.
b. The gravitational potential becomes zero.
c. The gravitational potential becomes infinite.
d. The gravitational potential decreases.

Answer 1

The gravitational potential at the surface of a sphere remains unchanged when a cavity within it is filled with denser material, as it only depends on the total mass and the distance to the center. Option A is correct.

Step-by-step explanation:

The question asks about changes in gravitational potential due to a spherical cavity that is filled with material of a higher density. When a hollow cavity inside a sphere is filled with a denser material, the mass inside the sphere increases, but the gravitational potential at the surface of the sphere remains the same.

This is because the gravitational potential at a point outside a spherical mass only depends on the total mass and the distance from the center, not how the mass is distributed inside. So, the correct answer is that the gravitational potential remains unchanged (option a).

The gravitational potential on the surface of an isolated uniform solid sphere remains unchanged when a spherical cavity is created inside the sphere, touching the surface of the original sphere, and filled with material of higher density. The gravitational potential is determined by the mass and radius of the object and does not depend on the presence or absence of a cavity or the material inside the cavity.