Question

A circular disc is rotating in horizontal plane about vertical axis passing through centre of disc without friction with a time period $0.2s$. If another identical circular disc is gently placed symmetrically on rotating disc, the time period of the combination of two discs is:

• A. $0.1s$
• B. $0.2s$
• C. $0.3s$
• D. $0.4s$

Answer 1

The correct option is D $0.4s$

Let the initial MI be $I$ and angular velocity be $\omega$,

so $T=2\pi /\omega =0.2s$

Now the final MI is $2I$, using Angular momentum conservation

We have $I\omega =2I{\omega }_1\Rightarrow {\omega }_1=\omega /2$

So new Time period $T_1=2\pi /{\omega }_1=2\pi /2\omega =0.4sec$