A weightless string can support a tension up to $30 \mathrm{~N}$. A stone of mass $0.5 \mathrm{~kg}$ is tied to its one end and is revolved in a circular path of radius $2 \mathrm{~m}$ in a vertical plane. Then the maximum angular velocity of the stone will be (acceleration due to gravity $g=10…

Question

A weightless string can support a tension up to $30 \mathrm{~N}$. A stone of mass $0.5 \mathrm{~kg}$ is tied to its one end and is revolved in a circular path of radius $2 \mathrm{~m}$ in a vertical plane. Then the maximum angular velocity of the stone will be (acceleration due to gravity $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Aicharya · Accepted Answer

Considering force balance: $\begin{aligned} & T_{\max }=m \omega_{\max }^2 r+m g \ & \Rightarrow \frac{T_{	ext {max }}}{m}=\omega_{\max }^2 r+g \ & \Rightarrow \frac{30 \mathrm{~N}}{0.5 \mathrm{~kg}}-10 \mathrm{~m} / \mathrm{s}^2=\omega_{\max }^2 r \ & \Rightarrow \omega_{\max }=\sqrt{\frac{50}{2}}=5 \mathrm{rad} / \mathrm{s}\end{aligned}$ .

A weightless string can support a tension up to $30 \mathrm{~N}$. A stone of mass $0.5 \mathrm{~kg}$ is tied…

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