Question

A block of mass of $10kg$ is in contact with the inner wall of a hollow cylindrical drum of radius $1m.$ The coefficient 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 $\left(g=10m/s^2\right)$

• A. $\sqrt{10}\frac{rad}{s}$
• B. $\frac{10}{2\pi }\frac{rad}{s}$
• C. $10\frac{rad}{s}$
• D. $10\pi \frac{rad}{s}$

Answer 1

The correct option is C $10\frac{rad}{s}$



$Limitingfriction,f_l=\mu N=\mu mr{\omega }^2(\because N=mr{\omega }^2)f_s=mg\text{For block to remain stationary,}{f}_s\le f_l\Rightarrow mg\le \mu mr{\omega }^2\Rightarrow \omega \ge \sqrt{\frac{g}{\mu r}}\Rightarrow {\omega }_{min}=10rad/s$