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Two masses m and (m)/(2) are connected a...

Two masses m and `(m)/(2)` are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is `tau=ktheta` for angular displacement `theta`. If the rod is rotated by `theta_(0)` and released, the tension in it when it passes through its mean position will be :

A

`(3 k theta_(0)^(2))/(l)`

B

`(k theta_(0)^(2))/(2l)`

C

`(2k theta_(0)^(2))/(l)`

D

`(k theta_(0)^(2))/(l)`

Text Solution

Verified by Experts

The correct Answer is:
D
`alpha=sqrt(k//I)`, `omega=theta_(0)xxalpha`
`T=momega^(2).(l)/(3)`
`impliesT=m.(l)/(3)theta_(0)^(2).(k)/(I)` `[ :. I=m.(l^(2))/(3)]`
`=(theta_(0)^(2)k)/(l)`
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