Calculating Gravitational Force on a Point Mass in the Presence of a Cavity

[maurice2705]

Homework Statement

The question is presented as picture.

Homework Equations

We do not have the radius of the cavity and the position of the m. How can we find the force acted on it?

The Attempt at a Solution

r=1/(M-m)*Ʃmr=1/(M-m)*4/3ρR'^3*r where m is the mass of cavity ,R' is the radius of the cavity and r is the position of center of mass. But I can't find R'.

 

[Filip Larsen]

Can you solve this problem if there was no cavity? If so, perhaps you can think of a way to model the problem so that the force on the point mass is the sum of two contributions, one from the big sphere and a "negative" from the small sphere?