Question

Two identical cylinder one rotating at angular speed $100\pi$ rad/s is brought in contact with other cylinder at rest, surface of both cylinders are rough. If $\alpha =2\pi rad/s^2$ is common angular acceleration/deceleration, then

• A. Time after which they acheive equal angular speed is $50s$
• B. Time after which they acheive equal angular speed is $25s$
• C. Angular speed (common) is $25\pi rad/s$
• D. Angular speed (common) is $50\pi rad/s$

Answer 1

Answer: (B), (D)

The correct options are
B Time after which they acheive equal angular speed is $25s$
D Angular speed (common) is $50\pi rad/s$

Conservation of angular momentum
$I{\omega }_0=2I\omega$
$\Rightarrow \omega =50\pi$

Common angular speed = $50\pi rad/s$
Also$\omega ={\omega }_0-\alpha t,$ for the first cylinder
$\Rightarrow 50\pi =100\pi -2\pi t\therefore t=25s$