A block of mass $10\; \mathrm{kg}$ is in contact against the inner wall of a hollow cylindow cylindrical drum of radius $1 \;\mathrm{m}$. The coeffident of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ......$rad/s$ $\left(g-10 m / s^{2}\right)$
NEET 2019, Medium
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$f_{L}=\mu N=\mu m r \omega^{2}$
$\mathrm{f}_{\mathrm{s}}=\mathrm{mg}$
As $\mathrm{f}_{\mathrm{s}} \leq \mathrm{f}_{\mathrm{L}}$
$\Rightarrow \mathrm{mg} \leq \mu \mathrm{mr} \mathrm{ \omega}^{2}$
$\Rightarrow \omega \geq \sqrt{\frac{g}{\mu r}}$
$\Rightarrow \omega_{\min }=10\; \mathrm{rad} / \mathrm{s}$
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