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 one end and sticks to it. Determine the velocity of the rod's center of mass and its angular velocity around the center post-collision.

• A. $v_{cm}=\frac{mv}{M+m},\ \omega _{final}=\frac{60mv}{L\left[25M+37m\right]}$
• B. $v_{cm}=\frac{Mv}{M+m},\ \omega _{final}=\frac{60m}{L\left[25M+37m\right]}$
• C. $v_{cm}=\frac{mv}{2\left(M+m\right)},\ \omega _{final}=\frac{60mv}{L\left[25\left(M+m\right)\right]}$
• D. $v_{cm}=\frac{2mv}{M+m},\ \omega _{final}=\frac{30mv}{L\left[25M+37m\right]}$

Answer: (A)