A wooden log of mass M and length L is hinged by a frictionless nail at O.A bullet of mass m strikes with velocity v and sticks to it. Find angular velocity of the system immediately after the collision aboutO.

Answer

A, C

Explanation

We know that `tau = (dvacL)/(dt)`
`tauxxdt = dvecL`
when angular impulse `(tauxxd vect)` is zero, the anglar
momentum is constant. In this case for the wooden
log-bullet system the angular impulse about O is constant .
therefore.
`[angular momentum of the system]_(initial]`
`=[angular momentum of the system]_(inital)`
`rArr mvxxL = I_0xxomega .....(i)`
where `I_0` is the moment of inertia of the wooden log - bullet
system after collision aobut O
`I_0 = I_(wooden log) + I_(bullet)`
`=(1)/(3)ML^2 +ML^2....(ii)`
From (i) and (ii)
`omega = (mvxxL)/([(1)/(3)ML^2 +mL^2]`
`rArr oemga = (mv)/([ML)/(3) + mL)]` = (3mv)/((M+3m))L)`