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A ball of mass (m) 0.5g is attached to t...

A ball of mass (m) 0.5g is attached to the end of a string having length (L) 0.5m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324N. The maximum possible value of anguar velocity of ball(in radian/s) is

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From figure `R=L sin theta` the horizontal component of tension T provides the necessary centripetal force
`therefore T sin theta=m omega^2 R`
`T sin theta= m omega^2 L sin theta`
`T=m omega^2 L or omega=sqrt(T/(mL))`
Substituting the given values ,we get
`omega=sqrt((324)/(0.5 times 0.5))=36 rad//s`
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