Question

A stone of mass $1000g$ tied to a light string of length $10/3m$ is whirling in a vertical circle. If the ratio of the maximum tension to minimum tension is $4$ and $g=10{ms}^{-2}$, then the speed of stone at the highest point of circle is :

• A. $20{ms}^{-1}$
• B. $10\sqrt{3}{ms}^{-1}$
• C. $5\sqrt{3}{ms}^{-1}$
• D. $10{ms}^{-1}$

Answer 1

Answer: (D)

$10{ms}^{-1}$

Minimum tension is at topmost point of the circle
Maximum tension is bottom point of the circle.
$\frac{Max.Tension}{Min.Tension}=\frac{\frac{m{v}_b^2}{r}+mg}{\frac{m{v}_t^2}{r}-mg}=4$
and
Conservation of energy is :
$\frac{v_b^2-v_t^2}{2}=2gr$
Using both equations,
$v_t^2=3gr$
So
$v_t=\sqrt{3gr}=10m/s$