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A uniform rod of mass m length l is atta...

A uniform rod of mass m length `l` is attached to smooth hinge at end A and to a string at end B as shown in figure. It is at rest. The angular acceleration of the rod just after the string is cut is :

A

`T=(3mg)/13`

B

`a_(A)=(3g)/13`

C

`T=(4mg)/13`

D

`a_(A)=(3sqrt(3)g)/13`

Text Solution

Verified by Experts

The correct Answer is:
C, D
`mg-T=ma`
`T l/2 cos theta=(ml^(2))/12 alpha`
By constraints,
`a=(alpha l)/2 costheta`
Thus, `T=(mg).(1+3cos^(2)theta)` and `a_(A)=(3gsinthetacostheta)/(1+3cos^(2)theta)`
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