the figure shows a spherical hollow inside a lead sphere of R=4.3m. the surface

Question

the figure shows a spherical hollow inside a lead sphere of R=4.3m. 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=217kg. With what gravitational force does the hollowed out lead sphere attract a small sphere of m=49kg that lies at d=12m from the center of sphere?

the figure shows a spherical hollow inside a lead sphere of R=4.3m. 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=217kg. With what gravitational force does the hollowed out lead sphere attract a small sphere of m=49kg that lies at d=12m from the center of sphere?

Explanation / Answer

Radius of cavity

r=R/2

The material that fill it has same density as the solid sphere

Mc/r3 =M/R3

So Mass of cavity is

Mc=[(R/2)2/R3]M =M/8

The magnitude of force that lead sphere exerts on m if

F1=GMm/d2

Part of this force is due to material that is removed.The center of the cavity is

d-r =d-R/2 from m ,so the force it exerts on m is

F2=G(M/8)m/(d-R/2)2

The Fore on the hollowed sphere on m is

F=F1-F2 =GMm/d2 -G(M/8)m/(d-R/2)2

F=(6.67*10-11)(217)(49)[1/122 -1/8(12-(4.3/2))2]

F=4.01*10-9 N

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