Consider a uniform rod of mass $M = 4 m$ and length $l$ pivoted about its centre. A mass $m$ moving with velocity $v$ making angle $\theta = \frac { \pi } { 4 }$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:
(1) $\frac { 3 } { 7 \sqrt { 2 } } \frac { v } { l }$
(2) $\frac { 3 } { 7 } \frac { v } { l }$
(3) $\frac { 3 \sqrt { 2 } } { 7 } \frac { v } { l }$
(4) $\frac { 4 } { 7 } \frac { v } { l }$