Rotational Motion

JEE Main level, single correct, medium

152 of 280

Question 152 of 280

A ball of mass 0.5kg0.5kg is attached to a string of length 50cm50cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400N400N. The maximum possible value of angular velocity of the ball in rads−1rad{s}^{-1} is,:

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Answer: (B) 4040

Let the string makes angle θ\theta with the vertical. Weight will be balanced by the vertical component of tension, which is Tcos⁡θ=mgT\cos \theta =mg and the horizontal component towards the centre will provide the required centripetal force for circular motion. Therefore,
Tsin⁡θ=mω2(lsin⁡θ)T\sin \theta =m{\omega }^{2}\left(l\sin \theta \right), where l=l=length of the string.
⇒400sin⁡θ=0.5ω2×0.5sin⁡θ\Rightarrow 400\sin \theta =0.5{\omega }^{2}\times 0.5\sin \theta
⇒ω=40rads−1\Rightarrow \omega =40rad{s}^{-1}

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