The figure shows a spherical hollow inside a lead sphere of radius R = 2.7 m; th

Question

The figure shows a spherical hollow inside a lead sphere of radius R = 2.7 m; the surface of the hollow passes through the center of the sphere and

The figure shows a spherical hollow inside a lead sphere of radius R = 2.7 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 = 214 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 32 kg that lies at a distance d = 15 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?

Explanation / Answer

F1 = G M1 m / R1^2    where M1 = 214 kg and R1 = 15 m

Now subtract the force that would have been due to the portion that

has been hollowed out

F2 = G M2 m / R2^2   where R2 = (15 - 2.7 / 2) = 13.65 m

F = G m (M1 / R1^2 - M2 - R2^2)

V1 / V2 = R1^3 / R2^3 =  (2.7 / 1.35)^3 = 8

So M2 = M1 / 8

F = G m M1 (1 / 15^2 - 1 / (8 * 13.65^2))

Now substitute and solve

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