Previous Year NEET Question- Laws Of Motion L-6

Question: the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$#

A) $\frac{10}{2 \pi} \mathrm{rad} / \mathrm{s}$

B) $10 \mathrm{rad} / \mathrm{s}$

C) $10 \pi \mathrm{rad} / \mathrm{s}$

D) $\sqrt{10} \mathrm{rad} / \mathrm{s}$

Answer: $10 \mathrm{rad} / \mathrm{s}$#

Solution:#

$$ \mathrm{f}{\mathrm{L}}=\mu \mathrm{N}=\mu \mathrm{mr} \omega^2 $$ $$ \mathrm{f}{\mathrm{s}}=\mathrm{mg} $$

As, $\mathrm{f}{\mathrm{s}} \leq \mathrm{f}{\mathrm{L}}$ $$ \Rightarrow \mathrm{mg} \leq \mu \mathrm{m}g \frac{v^2}{r} $$ $$ \Rightarrow \omega \geq \sqrt{\frac{g}{\mu r}} $$ $$ \Rightarrow \omega_{\min } \geq \sqrt{\frac{10}{0.1 \times 1}}=10 $$