Q: Two points P and *Q*, diametrically opposite on a disc of radius R have linear velocities *v* and 2*v* as shown in figure. Find the angular speed of the disc.

(a) $\displaystyle \frac{2v}{R} $

(b) $\displaystyle \frac{v}{R} $

(c) $\displaystyle \frac{v}{3R} $

(d) $ \displaystyle \frac{v}{2R} $

Ans: (d)

$ \displaystyle v_{cm} – \omega R = v $ …(i)

$ \displaystyle v_{cm} + \omega R = 2v $ …(ii)

From (ii)-(i)

$ \displaystyle 2\omega R = v $

$ \displaystyle \omega = \frac{v}{2R} $