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A spherical bob of mass $250 \mathrm{~g}$ is attached to the end of a string having length $50 \mathrm{~cm}$. The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is $72 \mathrm{~N}$. The maximum possible value of angular velocity of bob (in $\mathrm{rad} / \mathrm{s}$ ) is
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1661 Upvotes
Verified Answer
The correct answer is:
24
We have
$$
\begin{aligned}
\mathrm{T}_{\max } & =\mathrm{m} \omega_{\max }^2 \mathrm{R} \\
\omega_{\max } & =\sqrt{\frac{\mathrm{T}_{\max }}{\mathrm{mR}}}=\sqrt{\frac{72}{0.25 \times 0.5}}=24 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
$$
\begin{aligned}
\mathrm{T}_{\max } & =\mathrm{m} \omega_{\max }^2 \mathrm{R} \\
\omega_{\max } & =\sqrt{\frac{\mathrm{T}_{\max }}{\mathrm{mR}}}=\sqrt{\frac{72}{0.25 \times 0.5}}=24 \mathrm{rad} / \mathrm{s}
\end{aligned}
$$
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