Question

The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3 then its velocity is

• A. $\sqrt{98}$ m/s
• B. 7 m/s
• C. $\sqrt{490}$ m/s
• D. $\sqrt{4.9}$

Answer 1

The correct option is A $\sqrt{98}$ m/s

In this problem it is assuemed that particle although moving in a vertical loop but its speed remain constant.
Tenstion at lowest point $T_{max}$ = $\frac{m{v}^2}{r}$ + mg
Tension at highest point $T_{min}$ = $\frac{m{v}^2}{r}$ - mg
$\frac{T_{max}}{T_{min}}$ = $\frac{\frac{m{v}^2}{r}+mg}{\frac{m{v}^2}{r}-mg}$ = $\frac{5}{3}$
by solving we get , v=$\sqrt{4gr}$ = $\sqrt{4\times 9.8\times 2.5}$ = $\sqrt{98}$ m/s