Question

A weightless thread can withstand tension upto $30N$. A stone of mass $0.5kg$ is tied to it and is revolved in a circular path of radius $2m$ in a vertical plane. If $g=10m/s^2$, then the maximum angular velocity of the stone will be

• A. $5rad/s$
• B. $\sqrt{30}rad/s$
• C. $\sqrt{60}rad/s$
• D. $10rad/s$

Answer 1

The correct option is A $5rad/s$

Given : $T_{max}=30$ N $m=0.5kg$ $r=2$ m $g=10m/s^2$

Tension in the string is maximum when the stone is at the lowest position of the vertical motion.

Let the maximum angular velocity be $w_{max}$.

Using circular motion equation : $mr{w}_{max}^2=T_{max}-mg$

$\therefore$ $0.5\times 2\times w_{max}^2=30-0.5\times 10$

OR $w_{max}^2=30-5=25$ $⟹w_{max}=5$ $rad/s$