Q. A stone of mass 1 kg tied to a light inextensible string of length $L = \frac{10}{3}$ is whirling in a circular path of radius $L$ in vertical plane. If the ratio of the maximum tension to the minimum tension in the string is 4. What is the speed of stone at the highest point of the circle? (Taking $g = 10ms^{- 2}$)
A) 10 $ms^{- 1}$
B) 5$\sqrt{2}\ ms^{- 1}$
C) 10$\sqrt{3}\ ms^{- 1}$
D) 20$\ ms^{- 1}$
Explanation
(a) $\frac{T_{\max}}{T_{\min}} = \frac{\frac{mv^{2}}{L} + mg}{\frac{mv^{2}}{L} - mg} = 2\ $ …(i)
Simplifying Eq. (i), we get,
$v_{H} = \sqrt{3gL} = \sqrt{\frac{3 \times 10 \times 10}{3}} = 10\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.