Question

A weightless thread can bear tension upto $3.7kg$-wt. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $4m$ in a vertical plane. If $g=10m{s}^{-2}$, then the maximum angular velocity of the stone will be :

• A. 4 rad/s
• B. 16 rad/s
• C. $\sqrt{21}$ rad/s
• D. 2 rad/s

Answer 1

Answer: (A)

Tension in thread in vertical circular motion is maximum at the lowest point.
At the lowest point of vertical circular motion
$T_{\max }=mg+\frac{m{v}^2}{r}$
or $T_{\max }=mg+mr{\omega }^2$ ...(i)
Given, $T_{\max }=3.7\times 10=37N$
$mg=0.5\times 10=5N$
Thus, Eq. (i), becomes
$37=5+0.5\times 4\times {\omega }^2$
or ${\omega }^2=\frac{37-5}{0.5\times 4}=\frac{32}{2}=16$
or $\omega =4rad/s$