Question

An object is tied to a string and rotated in a vertical circle of radius $r$. Constant speed is maintained along the trajectory.

If $\frac{T_{\max }}{T_{\min }}=2,$ where, $T_{\max }=$ maximum tension and

$T_{\min }=$ minimum tension, then $\frac{v^{2}}{r g}$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

At the lowest point, $\frac{m v^{2}}{r}=T_{L}-m g\dots $(i)
At the highest point, $\frac{m v^{2}}{r}=T_{H}+m g \dots$(ii)
As $\frac{T_{\max }}{T_{\min }}=\frac{T_{L}}{T_{H}}=2 \therefore T_{L}=2 T_{H}$
As according to question, constant speed is maintained, therefore from equations (i) and (ii), we get
$T_{L}-m g=T_{H}+m g $ or $2 T_{H}-m g=T_{H}+m g$
or $T_{H}=2\, m g$
From equation (ii),
$\frac{m v^{2}}{r}=3 m g$ or $\frac{v^{2}}{r g}=3$