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 mass particle of m a distance d from the center, outside the inner radius, is:

Question

Quizplus · Accepted Answer

According to the shell theorem, for a spherically symmetric mass distribution, the gravitational force exerted by the shell on a particle located outside the shell depends only on the total mass M enclosed by the shell and the distance d from the center of the shell to the particle, and not on the distribution of mass within the shell. The shell can be treated as a point mass located at the center of the shell. Therefore, the magnitude of the gravitational force exerted on the shell by the point mass particle is given by: F = GMm/d^2 where G is the gravitational constant. Since the point mass particle is located outside the inner radius of the shell, we have d > R₁. Therefore, the correct choice is C: GMm/d.

A Spherical Shell Has Inner Radius R1, Outer Radius R2

A Spherical Shell Has Inner Radius R₁, Outer Radius R₂