A weightless thread can bear tension upto 37 N . A stone of mass...

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 \mathrm{~ms}^{-2}

, then the maximum angular velocity of the stone will be

Options

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

Correct answer

B. $4 \mathrm{rad} \mathrm{s}^{-1}$

Step-by-step solution

Maximum tension in the thread is given by or

T_{\max }=m g+\frac{m v^2}{r}

\quad T_{\max }=m g+m r \omega^2 (\because v=r \omega) or \quad \omega^2=\frac{T_{\max }-m g}{m r}

Given,

\begin{aligned} & T_{\max }=37 \mathrm{ N}, m=500 \mathrm{ g}=0.5 \mathrm{ kg}, g=10 \mathrm{ ms}^{-2}, \\ & r=4 \mathrm{ m} \\ & \therefore \quad \omega^2=\frac{37-0.5 \times 10}{0.5 \times 4}=\frac{37-5}{2} \\ & \text{ or } \quad \omega^2=16 \text{ or } \omega=4 \mathrm{rad} \mathrm{s}^{-1} \end{aligned}

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