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Physics-

General

Easy

Question

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

9
18
27
36

The correct answer is: 36

$T sin invisible function application theta equals m L sin invisible function application theta omega to the power of 2 end exponent$
$324 equals 0.5 cross times 0.5 cross times omega to the power of 2 end exponent$
$rightwards double arrow omega to the power of 2 end exponent equals fraction numerator 324 over denominator 0.5 cross times 0.5 end fraction$
$rightwards double arrow omega equals square root of fraction numerator 324 over denominator 0.5 cross times 0.5 end fraction end root$
$rightwards double arrow omega equals fraction numerator 18 over denominator 0.5 end fraction equals 36 blank r a d divided by s e c$

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