I need help calculating gravitational force. The figure shows a spherical hollow

Question

I need help calculating gravitational force.

The figure shows a spherical hollow inside a lead sphere of radius R = 4.8 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 = 372 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 12 kg that lies at a distance d = 18 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?

Explanation / Answer

given the mass of the sphere beofre altering is M = 372 kg

now the mass of adjusted sphere is

= 372 X (1 - (2/4)3) = 372X(1-1/8) = 372 X 0.875 = 325.5 kg

and the following mass is removed

mremoved = 372X1/8= 46.5 kg

and other mass is also given then m = 12 kg

gravitational force F = (GMm /d2) - (Gmremovedm /r2 )

F = ( 6.67 X 10-11 X 325.5 X 12 / 182 ) - ( 6.67 X 10-11 X 46.5 X 12 / 4.82 )

F = ((26053.02/324)-(3738.6/23.04)) 10-11

F = ( 80.41 - 162.26 ) 10-11

F = - 81.85 X 10-11 N in upward direction

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