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Physics-

General

Easy

Question

A ball of mass $open parentheses m close parentheses 0.5$ kg is attached to the end of a string having length $left parenthesis L right parenthesis$ 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is

9
18
27
36

The correct answer is: 36

$T cos invisible function application theta$ component will cancel $m g.$

$T sin invisible function application theta$ Component will provide necessary centripetal force the ball towards center C.
$therefore T sin invisible function application theta equals m r omega to the power of 2 end exponent equals m left parenthesis l sin invisible function application theta right parenthesis omega to the power of 2 end exponent$
$o r blank T equals m l omega to the power of 2 end exponent ⟹ omega equals square root of fraction numerator T over denominator m l end fraction end root r a d divided by s$
$o r blank omega subscript m a x end subscript equals square root of fraction numerator T subscript m a x end subscript over denominator m l end fraction equals square root of fraction numerator 324 over denominator 0.5 cross times 0.5 end fraction equals 36 blank r a d divided by s end root end root$

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