Question

A particle is moving in a vertical circle. The tension in the string when passing through two positions at angles ${30}^o$ and ${60}^o$ 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)

$T_1>T_2$

From the Free Body Diagram we get,

$T=\frac{m{v}^2}{r}+mgcos\theta$

At $\theta ={30}^{0}T=T_1=\frac{m{v}^2}{r}+\frac{\sqrt{3}mg}{2}$

At $\theta ={60}^{0}T=T_2=\frac{m{v}^2}{r}+\frac{mg}{2}$

From Above we get

$T_1>T_2$