Question

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

• A. $15m/s$
• B. $7m/s$
• C. $10m/s$
• D. $10m/s$

Answer 1

The correct option is C $10m/s$

Given,
Circle of radius $=2.5m$
Velocity is in the ratio $=5:3$
It is assumed that particle although moving in a vertical loop, but its speed remains constant.


Tension at lowest point,
$T_{max}=\frac{m{v}^2}{r}+mg$
Tension at highest point,
$T_{min}=\frac{m{v}^2}{r}-mg$

$\frac{T_{max}}{T_{min}}=\frac{\frac{m{v}^2}{r}+mg}{\frac{m{v}^2}{r}-mg}=\frac{5}{3}$

$3(\frac{m{v}^2}{r}+mg)=5(\frac{m{v}^2}{r}-mg)$

$\frac{3m{v}^2}{r}+3mg=\frac{5m{v}^2}{r}-5mg$
$8mg=\frac{2m{v}^2}{r}$
$4gr=v^2$
$v=\sqrt{4gr}=\sqrt{4\times 10\times 2.5}=10m/s$

Final Answer: (A)