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- Homework Statement
- A spherical hollow is made in a lead sphere of radius R, such that its surface touches the outside surface of the lead sphere and passes through its centre. The mass of the sphere before hollowing was M. With what force, according to the law of universal gravitation, will the hollowed lead sphere attract a small sphere of mass m, which lies at a distance d from the centre of the lead sphere on the straight line connecting the centres of the spheres and of the hollow?

(diagram below)

- Relevant Equations
- F = G*m1m2/r

I solved that the hollowed out mass is M/8, which is correct. I don't understand why it is incorrect to substitute the remaining mass (7M/8) back into the F = G*m1m2/r to produce the force. Why is the solution the force of the whole lead sphere minus the force of the “hole” lead sphere, which is

Thank you.