Question

A stone of mass $1kg$ tied to a light inextensible string of length $L=\frac{10}{3}m$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum is $4$ and if $g$ is taken to be $10m/s^2$, then speed of stone at the highest point of the circle is

• A. $20m/sec$
• B. $10\sqrt{3}m/sec$
• C. $5\sqrt{2}m/sec$
• D. $10m/sec$

Answer 1

The correct option is D $10m/sec$

Let '$v$' be the velocity at the top point
Velocity at the bottom point is $=v^2+2gd$ $=v^2+4gr$
Maximum tension in string appears when the stone is at the bottom of the circle.

$T_{max}=\frac{m(v^2+4gr)}{r}+mg$

Minimum tension appears in a string when the stone is at the top of the circle.

$T_{min}=\frac{m{v}^2}{r}-mg$

$\frac{T_{max}}{T_{min}}=\frac{\frac{v^2+4gr}{r}+g}{\frac{v^2}{r}-g}$ $=4$

On solving the equation we get, $v$$=10m/s$