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 ends what would be it angular velocity?

Options

A. V/L
B. 2V/L
C. V/3L
D. V/4L

Answer

C

Explanation

The impact force F = `(Deltap//Deltat)`, where `Deltap` = change of momentum of water of mass `Deltam` striking the ball with a speed v during time `Deltat`. Since water falls dead after collision with the ping-pong ball
`" "Deltap=Deltamv implies F = v (Deltam)/(Deltat)`
where `(Deltam)/(Deltat)` = rate of flow of water in the nozzle.
Since the ball is in equilibrium
`F - mg = 0 implies F = mg implies (vDeltam)/(Deltat) = mg implies (Deltam)/(Deltat) = (mg)/(v)`