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

A

Explanation

Change an angular momentum of the system` =`angular impulse given to the system `("angular momentum")_f-("angular momenum")_I`
`=MVxxL/2` …..i
Let the system starts rotating with the angular velocity `omega`. Momentun of inertia of the system about its axis of rotation. (centre of mass of system) `=M(L/2)^(2)+M(L/2)^(2)=(2ML^(2))/4`
`=(ML^(2))/2` (from i)
`Iomega-0=MVxL/2`
`impliesomega=(MV)/IxxL/2=(MV)/((ML^(2))//2)xxL/2=V/L`