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A small ring P is threaded on a smooth w...

A small ring P is threaded on a smooth wire bent in the form of a circle of radius a and centre O. The wire is rotating with constant angular speed `omega` about a vertical diameter xy, while the ring remains at rest relative to the wire at a distance `(a)/(2)` from xy. Then is equal to:

A

`(2g)/(a)`

B

`(g)/(2a)`

C

`(2g)/(asqrt(3))`

D

`(g sqrt(3))/(2a)`

Text Solution

Verified by Experts

The correct Answer is:
C

`N cos theta = mg` …(i) and `N sin theta = (m omega^(2) a)/(2)` ….(ii)
Equation (ii) divided by equation (i)
`tan theta = (omega^(2) a)/(2g)`, `omega^(2) = (2g tan theta)/(a)`, `sin theta = (a)/(2) xx (1)/(a) = (1)/(2)` , `theta = 30^(@)`
`omega^(2) = (2 g tan 30^(@))/(a)` , `omega^(2) = (2g)/(sqrt(3) a)`
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