A ball of mass $0.5kg$ is attached to the end of a string having length $0.5m.$ 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 angular velocity of ball (in $rad/s$) is:

A

$9$

B

$18$

C

$27$

D

$36$

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Solution

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Correct option is D)

We have, $Tsinθ=mrω_{2}$ But, $sinθ=Lr $ $∴T=mLω_{2}$ $∴324=0.5×0.5×ω_{2}$ $∴ω=36rad/s$