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In the figure shown there is a smooth tu...

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 the end 'C' of the spring is fixed and the end A is free Initially the line OA makes an angle of `60^(@)` with OC and finally it makes an angle of `30^(@)` after compression find the spring constant of the spring

A

`(12mg(2+sqrt(3)))/(pi^(2)R)`

B

`(36mg(2+sqrt(3)))/(pi^(2)R)`

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
By energy conservation mgR ` (1+cos 30^(@))=1/2k (((piR)/3)^(2)-((piR)/6)^(2))`
` Rightarrow k= (12mg(2+sqrt(3)))/(pi^(2)R`
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