IIT-JEE 2011 · Paper 1 · Physics Q28

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A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 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 radian/s) is

A conical pendulum: a string of length L hangs from a ceiling and the ball m moves in a horizontal circle about the vertical dashed axis through the point of suspension.

Answer and worked solution

Official answer: D

Conical pendulum. The horizontal component of tension gives the centripetal force: $T\sin\theta=m\omega^2L\sin\theta$ , so $T=m\omega^2L$ .

Maximum. $\omega^2=\dfrac{324}{0.5\times0.5}=1296$ , $\omega=36$ rad/s.

(D)

Topics:Circular motion dynamics Stress and strain

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IIT-JEE 2011 · Paper 1, Physics question 28