A slender, uniform copper rod with mass M and length L is positioned on a frictionless horizontal plane. A moist clay ball with mass m, traveling at speed v, strikes the rod at a point one-fifth its length from the rod's center of mass and sticks to it. Determine the velocity of the combined system's center of mass and its angular velocity around the center post-collision.

$v_{cm}=\frac{mv}{M+m},{\omega }_{final}=\frac{60mv}{L[25M+37m]}$

$v_{cm}=\frac{Mv}{M+m},{\omega }_{final}=\frac{60m}{L[25M+37m]}$

$v_{cm}=\frac{mv}{2(M+m)},{\omega }_{final}=\frac{60mv}{L\left[25(M+m)\right]}$

$v_{cm}=\frac{2mv}{M+m},{\omega }_{final}=\frac{30mv}{L[25M+37m]}$