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A cavity of radius R//2 is made inside a...

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 centre of the cavity)
[Here g`=(GM)//R^(2)`, where M is the mass of the sphere

A

`(mg)/(2)`

B

`(3mg)/(8)`

C

`(mg)/(16)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Mass of sphere `M prop R^(3)`. If mass of complete sphere is M, then, the mass of cavity will be `M//8`.
Using the figure, F=Force due to whole sphere-Force due to cavity
`F=(GMm)/(R^(3))-((R )/(2))-(G(M//8)m)/((R^(2)))`
`=(GM m)/(R^(2))[(4)/(8)-(1)/(8)]=(3)/(8)(GM m)/(R^(2))=(3)/(8)mg`
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