Q. A weightless thread can support tension upto $30\ N$. A stone of mass $0.5\ kg$ is tied to it and is revolved in a circular path of radius $2\ m$ in a vertical plane. If $g = 10\ m/s^{2}$, then the maximum angular velocity of the stone will be
A) $5\ rad/s$
B) $\sqrt{30}\ rad/s$
C) $\sqrt{60}\ rad/s$
D) $10\ rad/s$
Explanation
(a) $T_{\max} = m\omega_{\max}^{2}r + mg\ \Rightarrow \frac{T_{\max}}{m} = \omega^{2}r + g$
$\Rightarrow \frac{30}{0.5} - 10 = \omega_{\max}^{2}r \Rightarrow \omega_{\max} = \sqrt{\frac{50}{r}} = \sqrt{\frac{50}{2}} = 5\ rad/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.