Gravitational Force of a Point Particle Between Two Spherical Shells

[Ishida52134]

Homework Statement

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

Homework Equations

F = -GMm/r^2

The Attempt at a Solution

I know that from gauss's law that the force from a spherical shell would have the same gravitational force as one from a point particle. How would you find the gravitational force of a particle located between two shells though?

 

[Ishida52134]

any ideas

 

[haruspex]

I know that from gauss's law that the force from a spherical shell would have the same gravitational force as one from a point particle.

That's only true for points outside the shell. What is the force on a particle entirely inside the shell?

 

[Ishida52134]

0. Oh do you just find the force and use density = m/v to substitute m with pv.
Then v = 4/3 pi r^3. Then u just subtract the total volume of the sphere by the volume of the sphere with distance d < the particle.

 

[haruspex]

0. Oh do you just find the force and use density = m/v to substitute m with pv.
Then v = 4/3 pi r^3. Then u just subtract the total volume of the sphere by the volume of the sphere with distance d < the particle.

I'm not completely sure what you are saying there, but it doesn't sound quite right.
Think of the given shell annulus as made up of two shell annuli: one with outer radius d and one with inner radius d.