Question

A weightless thread can bear tension upto $3.7\, kg$-wt. A stone of mass $500\, g$ is tied to it and revolved in a circular path of radius $4\, m$ in a vertical plane. If $g=10\, ms ^{-2}$, 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
$T_{\max }=m g+\frac{m v^{2}}{r}$
or $T_{\max }=m g +m r \omega^{2}$ ...(i)
Given, $T_{\max } =3.7 \times 10=37\, N$
$m g =0.5 \times 10=5\, N$
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 $\omega=4\, rad / s$