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. $T_1>T_2$
• C. $T_1<T_2$
• D. Tension in the string always remains the same

Answer 1

Answer: (B)

$T=\frac{m{v}^2}{r}+mg\cos \theta$
For $\theta =30^{\circ }$,
$T_1=\frac{m{v}^2}{r}+mg\cos 30^{\circ }=\frac{m{v}^2}{r}+\frac{\sqrt{3}mg}{2}\dots (i)$
For $\theta =60^{\circ }$
$T_2=\frac{m{v}^2}{r}+mg\cos 60^{\circ }=\frac{m{v}^2}{r}+\frac{mg}{2}\dots (ii)$
From equation (i) and (ii), we can say
$\therefore T_1>T_2$