Question

A bead of mass m is attached with a disc of mass M and radius R by an inextensible string wrapped over the disc. If the pivot is smooth and the string does not slide along the disc, after releasing the bead from rest. Find the angular speed (in rad/s) of the disc just after the string becomes taut. See figure as shown.
(Given : h = 5/2 m ; R = 25 cm ; m = 1 kg ; M = 2 Kg)

• A. 210
• B. 20
• C. 200
• D. 180

Answer 1

The correct option is B 20

$l=5$ $m=1$

$mgl=\frac{1}{2}m{v}^2$

$v=10$

Now conserving angular momentum

$I\omega =mvr$

$M{r}^2\omega =mvr$

$2\times .25\times .25\omega =1\times 10\times .25$

$\omega =20$