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 $\frac{v^2}{rg}$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

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