Question

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angle $30^{\circ}$ 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

Answer 1

Answer: (C)

Tension, $T=\frac{m v^{2}}{r}+m g \cos \theta$
For, $\theta=30^{\circ},$
$T_{1}=\frac{m v^{2}}{r}+m g \cos 30^{\circ}$
$\theta=60^{\circ}, T_{2}=\frac{m v^{2}}{r}+m g \cos 60^{\circ}$
$\therefore T_{1} >T_{2}$