A rod of mass m and length l in placed on a smooth table. An another particle of same mass m strikes the rod with velocity `v_(0)` in a direction perpendicular to the rod at distance `x( lt l//2)` from its centre . Particle sticks to the end. Let `omega` be the angular speed of system after collision , then
Find the maximum possible value of impulse (by varying x) that can be imparted to the particle during collision. Particle still sticks to the rod.

Options

A. `(mv_(0))/(2)`
B. `(2mv_(0))/(3)`
C. `(3mv_(0))/(4)`
D. `(4mv_(0))/(5)`

Answer

A