2019 Laws of MotionFriction and Circular Motion Medium Question 20 of 72 in Laws of Motion

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

The answer is C.

Solution

The normal reaction from the wall provides the centripetal force: $N=mr\omega^2$ For equilibrium of the block, limiting friction must balance weight: $f_L=\mu N\ge mg$ $\mu mr\omega^2\ge mg\Rightarrow\omega\ge\sqrt{\frac{g}{\mu r}}$ $\omega_{min}=\sqrt{\frac{10}{0.1\times1}}=10\ rad/s$

Concept minimum angular speed to keep a block against a rotating wall

Laws of Motion in past papers

72 questions from this chapter have appeared across 27 exam years.