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# A cavity of radius R/2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R/2 from the centre of the sphere. The gravitational force on a particle of mass 'm'at a distance R/2 from the centre of the sphere on the line joining both the centres of a sphere and cavity is - (opposite to the centre of gravity)[Here g=GM/R2, where M is the mass of the sphere]mg23mg8mg16None of these

A
3mg8
B
mg2
C
None of these
D
mg16
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=−−pR24ε0Net gravitational field¯E=¯E1+¯E2=pR6ε0−pR24ε0=pR8ε0Net force on m→F=m¯E=mpR8ε0Here, p=M(4/3)πR3 & ε0=14πGThen, F=3mg8

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