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[Here g=GM/R2, where M is the mass of the sphere]

- mg2
- 3mg8
- mg16
- None of these

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Solution

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Gravitational field at mass m due to full solid sphere

¯E1=p¯r3ε0=pR6ε0.......[ε0=14πG]

Gravitational field at mass m due to cavity (−p)

¯E2=(−p)(R/2)3¯r3ε0R2.......[usingE=pa33ε0r2]

−(−p)R324ε0R2=−−pR24ε0

Net gravitational field

¯E=¯E1+¯E2=pR6ε0−pR24ε0=pR8ε0

Net force on m→F=m¯E=mpR8ε0

Here, p=M(4/3)πR3 & ε0=14πG

Then, F=3mg8

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