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A uniform ring of mass M and radius R is...

A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of `d = sqrt(3)R` from the centre of the sphere. The gravitational attraction between the sphere and the ring is

A

`(GM^2)/(R^2)`

B

`(3GM^2)/(2R^2) `

C

`(2GM^2)/(sqrt2 R^2)`

D

`(sqrt3 GM^2)/(R^2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Gravitational intensity due to the ring at a distance d = `sqrt3R` on its axis is
`I = (GMd)/((d^2 + R^2)^(3//2)) = (GM xx sqrt3 R)/((3R^2 + R^2)^(3//2) ) = (sqrt3 GM)/(8R^2)`
Force on sphere ` = (8M)l = (8M) xx (sqrt3 GM)/(8R^2) =(sqrt3 GM^2)/(R^2)`
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