Q. A weightless thread can bear tension upto 37 N. A. stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. $If\ g = {10\ ms}^{- 2},$ then the maximum angular velocity of the stone will be
A) $2\ rad\ s^{- 1}$
B) $4\ rad\ s^{- 1}$
C) $8\ rad\ s^{- 1}$
D) $16\ rad\ s^{- 1}$
Explanation
(b) Maximum tension in the thread is given by
$T_{\max} = mg + \frac{{mv}^{2}}{r}$
$or\ T_{\max} = mg + {mrw}^{2}\ \ \ \ \ \ \ \ \ \ \ (\because v = r\omega)$
$or\ \ \omega^{2} = \frac{T_{\max} - mg}{mr}$
$Given,\ \ \ \ T_{\max} = 37\ N,\ m = 500g = 0.5\ kg,\ g = {mg}^{- 2},$
$r = 4m$
$\therefore\ \ \ \omega^{2} = \frac{37 - 0.5 \times 10}{0.5 \times 4} = \frac{37 - 5}{2}$
$or\ \ \omega^{2} = 16$
$or\ \omega = {4\ rad\ s}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.