Question

A block of mass $10\, kg$ is in contact against the inner wall of a hollow cylindrical drum of radius $1\,m$. 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 :
$(g = 10\ m/s^2)$

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

Answer 1

Answer: (A)

10 rad/s

Answer 2

For equilibrium of the block limiting friction
$f_{L} \ge mg$
$\Rightarrow \mu N \ge mg$
$\Rightarrow \mu mr\omega^{2} \ge mg$
$\omega \ge \sqrt{\frac{g}{r\mu}}$
$\omega_{min } =\sqrt{\frac{g}{r\mu}}$
$\omega_{min } = \sqrt{\frac{10}{0.1 \times1}} = 10$ rad/s

So, the correct option is (A): 10 rad/s