Question

In a gravity free space, a hollow cylinder of radius $4R$ and mass $M$ is being rotated with a constant angular velocity $\omega$ clockwise with respect to an inertial frame of reference. Another hollow cylinder of radius $R$ and mass $m$ is rotating inside this cylinder, such that it touches the inner surface of larger cylinder without slipping and its centre of mass appears stationary from inertial frame Dynamic friction coefficient between cylinders is $\mu$. If the normal reaction between cylinders is denoted by $N$, answer the following questions.


What is the angular velocity of smaller cylinder ?

• A. $4\omega$
• B. $\omega /3$
• C. $3\omega /4$
• D. $3\omega$

Answer 1

The correct option is A $4\omega$

For no slipping
$$v_1=v_2$$
$${\omega }^{\prime }R=\omega .4R$$
$${\omega }^{\prime }=4\omega$$.