$A$ bar of mass $M=1.00 \ kg$ and length $L=0.20 \ m$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. $A$ small mass $m=0.10 \ kg$ is moving on the same horizontal surface with $5.00 \ m \ s^{-1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L/2$ from the pivoted end and returns back on the same path with speed $v$. After this elastic collision,the bar rotates with an angular velocity $\omega$. Which of the following statements is correct?

• A
  $\omega=6.98 \ rad \ s^{-1}$ and $v=4.30 \ m \ s^{-1}$
• B
  $\omega=3.75 \ rad \ s^{-1}$ and $v=4.30 \ m \ s^{-1}$
• C
  $\omega=3.75 \ rad \ s^{-1}$ and $v=10.0 \ m \ s^{-1}$
• D
  $\omega=6.80 \ rad \ s^{-1}$ and $v=4.10 \ m \ s^{-1}$