Question

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, what would be its angular velocity ?

• A. v/L
• B. 2v/L
• C. v3L
• D. v/4L

Answer 1

Answer: (A)

v/L

Answer 2

Let $\omega$ be the angular velocity of the rod. Applying, angular impulse = change in angular momentum about centre of mass of the system
$j.\frac{L}{2}=I_c\omega$
$\therefore (Mv)\bigg(\frac{L}{2}\bigg)=(2)\bigg(\frac{ML^2}{4}\bigg)\omega$
$\therefore \omega=\frac{v}{L}$