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A thin horizontal uniform rod AB of mass...

A thin horizontal uniform rod `AB` of mass `m` and length `l` can rotate freely about a vertical axis passing through its end `A`. At a certain moment, the end `B` starts experiencing a constant force `F` which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. The angular velocity of the rod as a function of its rotation angle `theta` measured relative to the initial position should be.

Text Solution

Verified by Experts

Work done by the torque
`/_\W=int taudtheta=int_(0)^(theta)Flcosthetad theta`
`/_\W=Flsintheta`
Now using work energy theorem
`/_\W=/_\k`
`:.Flsintheta=[1/2((ml^(2))/3)omega^(2)-0]`
Which gives `omega=(sqrt(6Fsintheta)/(ml))`
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