Question

A weightless thread can bear tension upto 37 N. 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 $g=10\text{m}{\text{s}}^{-2},$ then the maximum angular velocity of the stone will be:

• A. $2\text{rad}{s}^{-1}$
• B. $4\text{rad}{s}^{-1}$
• C. $8\text{rad}{s}^{-1}$
• D. $16\text{rad}{s}^{-1}$

Answer 1

Answer: (B)

Maximum tension in the thread is given by $T_{\max }=mg+\frac{m{v}^2}{r}$ or $T_{max}=mg+mr{\omega }^2(\because v=r\omega )$ or ${\omega }^2=\frac{T_{\max }-mg}{mr}$ Given, $T_{\max }=37N,m=500g=0.5kg,g=10m{s}^{-2},$ $r=4m$ $\therefore$ ${\omega }^2=\frac{37-0.5\times 10}{0.5\times 4}=\frac{37-5}{2}$ or ${\omega }^2=16$ or $\omega =4rad{s}^{-1}$