Question

The gravitational field inside a hollow spherical shell is
(A) Zero
(B) Constant
(C) $ \propto \dfrac{1}{r}$
(D) $ \propto \dfrac{1}{{{r^2}}}$

Answer 1

Hint: We know that the gravitational force is the force that attracts two bodies. Gravitation is a natural process. All bodies in the universe by themselves have a gravitational force. According to classical mechanics, the gravitational force is a physical quantity and it is explained by Newton’s universal law of gravity.

Complete step by step solution:
The gravitational simplifications that can be applied to objects that are inside or outside a sphere can be explained by the shell theorem in classical mechanics. According to the shell theorem, spherically symmetric bodies will produce a gravitational field that affects all the external objects outside it as the mass is concentrated in a particular point in the spherically symmetric body. Also for a spherically symmetric body, there will not be any gravitational field experienced by the bodies inside the sphere. That means regardless of the position inside the spherical shell, objects inside the shell will not experience any gravitational force. Therefore the gravitational field inside a hollow spherical will be zero.

The answer is: Option (A): Zero

Additional information:
The gravitational field decreases with the increase of the distance from the center of mass and becomes zero at infinity. The gravitational field at any point on the surface of the earth is numerically equal to the value of $g$.

Note:
The space surrounding a body where its gravitational influence is felt is called the gravitational field. The intensity of the gravitational field at any point is defined as the gravitational force experienced by unit mass placed at that point. This is a vector quantity and is directed towards the center of the earth.