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A bead of mass m is attached to one end ...

A bead of mass m is attached to one end of a spring of natural length R and spring constant `K=((sqrt(3)+1)mg)/(R )`. The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in fig. The normal reaction at B just after it is released to move is

A

`(mg)/(2)`

B

`sqrt(3)mg`

C

`3sqrt(3)mg`

D

`(3sqrt(3)mg)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
The extension is spring is `x=2R cos 30^(@)-R=(sqrt(3)-1)R`

`kx cos 30^(@)+mg cos 30^(@)`
Applying Newton's second law to the bead normal to circular rind at point `B`
`N=K(sqrt(3)-1)R cos 30^(@)+mg cos 30^(@)`
`=((sqrt(3)-1))/(R) mg (sqrt(3)-1)R cos 30^(@)+mg cos 30^(@)`
`N=(3 sqrt(3)mg)/(2)`.
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