Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod…

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?

Numerical

(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 $

$\large \omega = \frac{v}{L}$