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A ring of mass m and radius R rests in e...

A ring of mass m and radius R rests in equilibrium on a smooth cone of semi-vertical angle `45^(@)` as shown. The radius of the cone is 2R. the radius of circular cross section of the ring is `r(r lt lt R)`.

What will be the tension in the ring?

A

`(mg)/(2sqrt(2)pi)`

B

`(mg)/(2pi)`

C

`(mg)/(sqrt(2)pi)`

D

`(sqrt(2)mg)/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
B
FBD of small section of ring subtending angle `d theta` at centre of ring is as shown.

`(N)/(sqrt(2))=T d theta, (N)/(sqrt(2))=(m d theta)/(2pi)g`
`rArr T=(mg)/(2pi)`
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