Gravitation, hollowed out sphere

[Puchinita5]

Homework Statement

Figure 13-39 shows a spherical hollow inside a lead sphere of radius R = 4.5 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 380 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 22 kg that lies at a distance d = 17 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c13/fig13_39.gif

The Attempt at a Solution

I attempted to figure out the mass of the hollowed out section by taking the density of the whole sphere and setting that equal to what the density of the small sphere would be and solving for mass. I got the mass for the hollowed section to be 47.5, so I subtracted this from the original mass to get the final mass. I then used F=G(m1)(m2)/r^2 to solve for force, using the final mass of the hollowed sphere. This gave me the wrong answer. The only thing I can think is that the center of mass would no longer be at the spheres center, so the distance between the two objects should be different, but I don't know how I would calculate where the center of mass would now be. Any insight?

 

[Puchinita5]

ok nevermind, i just figured it out...i took a wild guess how to do it and it worked, though i am not really sure why. I used the force equation for the orignal sphere, and then for the hollowed sphere. I subtracted the force of the hollowed sphere from the force of the orignal, and got the right answer. Doesn't wholly make sense to me