List-I, shows four system of rod + particle undergoing collision on a smooth horizontal floor. Mass of particle & rod in each case is m & M respectively. In List-II relationship between velocity (v) of centre of rod and angular velocity ($\omega$) of the rod just after the collision are given. Choose appropriate option (length of rod is $\mathcal{l}$)

	List-I		List-II
P)		(1)	$v=\frac{\omega \mathcal{l}}{3}$
Q)		(2)	$v=\frac{\omega \mathcal{l}}{2}$
R)		(3)	$v=\frac{\omega \mathcal{l}}{6}$
S)		(4)	$v=\frac{2\omega \mathcal{l}}{3}$