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In the figure shown, there is a smooth t...

In the figure shown, there is a smooth tube of radius `R`, fixed in the vertical plane. A ball `B` of mass `m` is released from the top of the tube. `B` slides down due to gravity and compresses the spring is fixed and end `A` is free., Initially, line `OA` makes an angle `60^@` with `OC` and finally it makes an angle of `30^@` after compression. Find the spring constant of the spring.

A

`(12 mg (2 + sqrt3))/(pi^(2) R)`

B

`(36 mg (2 + sqrt3))/(pi^(2) R)`

C

`(18 mg)/(pi^(2) R)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
By energy conservation
`mgR (1 + cos 30^(@)) = (1)/(2) k((pi R)/(6))^(2)`
`implies k = (36 mg (2 + sqrt(3)))/(pi^(2)R)`
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