How do we calculate gravitational force when an object is inside a shell?

[anhchangdeptra]

Imagine all the mass of the Earth is in a shell of a thickness of R(earth)/2. So if the object is inside the shell or outside the shell, I know I can apply the shell theorem to solve the gravitational force acting on it. But, what if the object is IN the shell, in another words R(earth)/2<r<R(earth), how do we calculate the gravitational force?

 

[jedishrfu]

so its like you have two shells. The object is outside one shell and inside the other. Apply the shell theorem to each one and what do you get.

 

[anhchangdeptra]

Oh! So we only care about the smaller shell with radius= R/2. The distance from mass m to the center is r so basically we have the same formula as for an object outside the bigger shell= (GMm)/r^2 (only the r is different is the two cases)?

 

[Bandersnatch]

Oh! So we only care about the smaller shell with radius= R/2. The distance from mass m to the center is r so basically we have the same formula as for an object outside the bigger shell= (GMm)/r^2 (only the r is different is the two cases)?

M is also different. After all, you don't care about the part of the shell above the object.

 

[anhchangdeptra]

Oh yes! I really forget the M. Thank you very much!