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A sphere of mass m attached with the fre...

A sphere of mass `m` attached with the free end of a steel wire of length `l` swings in the veritcle plane form the horizontal positon.

Elastic energy should in the wire in the vericle positon is

A

`(9m^(2) g^(2)l)/(2Ypi r^(2))`

B

`(7m^(2) g^(2)l)/(2Ypi r^(2))`

C

`(9m^(2) g^(2)l)/(Ypi r^(2))`

D

`(9m^(2) g^(2)l)/(4Ypi r^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
`Delta l = ((F_("net")l))/(YA) , V = sqrt(2gl)`
`= ((mg + (mv^(2))/(l))l)/(YA) = ((mg + 2mg)l)/(YA)`
`Deltas L = (3mgl)/(Y(pi r^(2))), v = (1)/(2)Fe, U = (YA)/(2l) xx (Delta l)^(2) = (9m^(2) g^(2) l)/(2Y pi r^(2))`
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