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A uniform ring of mass m and radius a is...

A uniform ring of mass `m` and radius `a` is placed directly above a uniform sphere of mass `M` and of equal radius. The centre of the ring is at distance `sqrt(3)a` from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

A

`(GMm)/(8r^(2))`

B

`(GMm)/(4r^(2))`

C

`sqrt(3)(GMm)/(8r^(2))`

D

`(GMm)/(8r^(3)sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
( c) `dF=G(Mdm)/(4r^(2))`
`F=sumdFcos theta`
`=sum(GMdm)/(4r^(2)) cos theta`
`=(GM)/(4r^(2))xx(sqrt(3)r)/(2r)sumdm`
`=(sqrt(3)GMm)/(8r^(2))`
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