The figure shows a spherical hollow inside a lead sphere of radius R = 4.9 m; th

Question

The figure shows a spherical hollow inside a lead sphere of radius R = 4.9 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 = 306 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 14 kg that lies at a distance d = 13 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow? Please provide numerical answer.

The figure shows a spherical hollow inside a lead sphere of radius R = 4.9 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 = 306 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 14 kg that lies at a distance d = 13 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow? Please provide numerical answer.

Explanation / Answer

Radius of hollowed out sphere = 4.9/2 = 2.45m Mass of hollowed out sphere = 306x(1/2)^3 = 306/8 Distance of hollowed out sphere from small sphere = d-R/2 = 10.55m Net Gravitational Force = G*306*14/13^2 - G*(306/8)*14/10.55^2 = G*14*306*[1/13^2 - 1/(8*10.55^2)] = 1.39x10-9N

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