A spherical hollow cavity 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 center. The mass of the sphere before hollowing was M. With what gravitational force will the hollowed-out lead sphere attract a small sphere of mass ‘ m ‘, which lies at a distance d from the center of the lead sphere on the straight line connecting the centers of the spheres and that of the hollow, if d = 2R:
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Gravitational field at ‘m’ due to hollowed - out lead sphere
= {Field due to solid spere} – {Field due to mass that was removed}
Field due to solid sphere = 
= E 1 = 
Field due to removed mass = 
= E 2
M’ = 
× 
= 
And x = d – 
So, E 2 = 
= 
= 
E net = E 1 – E 2 = 
= 
F net = mE net = 
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