A spherical shell has inner radius R₁, outer radius R₂, and mass M, distributed uniformly throughout the shell. The magnitude of the gravitational force exerted on the shell by a point particle of mass m, located a distance d from the center, outside the inner radius and inside the outer radius, is:

Question

Quizplus · Accepted Answer

By the shell theorem, the force exerted by the shell on the point particle is the same as if all the mass of the shell were concentrated at its center. Therefore, we can consider only the gravitational force exerted by a point mass M at the center of the shell.
The magnitude of this force on a mass m located a distance d from the center is given by the formula for gravitational force:
F = GMm/d^2
Substituting the values given,
F = G(Mm)/(d^2)
= GMm/(d^2).
Therefore, the answer is D.

A Spherical Shell Has Inner Radius R1, Outer Radius R2

A Spherical Shell Has Inner Radius R₁, Outer Radius R₂