Q: Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J=Mv is imparted to the body at one of its end, whet would be its angular velocity?
(a)v/L
(b)2v/L
(c)v/3L
(d)v/4L
Ans: (a)
Sol: Let ω = angular velocity of the rod
Angular Impulse = Change in angular moementum about COM of the system
$\large J(\frac{L}{2}) = I_{com}\omega $
$\large Mv(\frac{L}{2}) = (M\frac{L^2}{4} + M\frac{L^2}{4})\omega $
$\large Mv(\frac{L}{2}) = (M\frac{L^2}{2})\omega $
$\large \omega = \frac{v}{L}$