Q. A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30{^\circ}$ and $60{^\circ}$ from vertical (lowest position) are $T_{1}$ and $T_{2}$ respectively. then
A) $T_{1} = T_{2}$
B) $T_{2} > T_{1}$
C) $T_{1} > T_{2}$
D) Tension in the string always remains the same
Explanation
(c) Tension, $T = \frac{mv^{2}}{r} + mg\cos\theta$
$For,\ \theta = 30{^\circ},\ T_{1} = \frac{mv^{2}}{r} + mg\cos{30{^\circ}}$
$\theta = 60^{o},T_{2} = \frac{mv^{2}}{r} + mg\cos 60^{o}\therefore T_{1} > T_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.