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

Engineering

Physics

Circular Motion in Vertical Plane

Question

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T cos $θ$ = mg

T sin $θ$ = m $ω$ ²L sin $θ$

T = m $ω$ ²L

$ω_{\max}^{2} = \frac{T_{\max}}{mL}$

$ω_{\max} = \sqrt{\frac{T_{\max}}{mL}} = \sqrt{\frac{324}{0 .5 \times 0 .5}} = \sqrt{324 \times 4}$

= 36 rad/s