Consider a body, shown in Fig. 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 its angular velocity?

Options

A. `V/L`
B. `(2V)/L`
C. `V/(3L)`
D. `V/(4L)`

Answer

A

Explanation

Change in angular momentum of the system = angular impulse given to the system `=("angular momentum")_(f) -("angular momentum")_(I)`
`=MV xx L/2`………(i)
Let the system starts rotating with angular velocity `omega`.
Moment of inertia of the system about its axis rotation (centre of mass of the system).
`=M(L/2)^(2) + M(L/2)^(2) = (2ML^(2))/4 = (ML^(2))/2` From (i)
`I omega -0 = MV xx L/2 rArr omega = (MV)/IO xx L/2 = (MV)/(ML^(2)//2) xx L/2 = V/L`.