A bar of mass $M=1.00 \mathrm{kg}$ and length $L=0.20 \mathrm{m}$ 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 $m=0.10 \mathrm{kg}$ is moving on the same horizontal surface with $5.00 \mathrm{m} {\mathrm{s}}^{–1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $\frac{L}{2}$ 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 statement is correct?

• Correct answer
  A

  $\omega =6.98 \mathrm{rad} {\mathrm{s}}^{–1}$ and $v=4.30 \mathrm{m} {\mathrm{s}}^{–1}$
• B

  $\omega =3.75 \mathrm{rad} {\mathrm{s}}^{–1}$ and $v=4.30 \mathrm{m} {\mathrm{s}}^{–1}$
• C

  $\omega =3.75 \mathrm{rad} {\mathrm{s}}^{–1}$ and $v=10.0 \mathrm{m} {\mathrm{s}}^{–1}$
• D

  $\omega =6.80 \mathrm{rad} {\mathrm{s}}^{–1}$ and $v=4.10 \mathrm{m} {\mathrm{s}}^{–1}$

Hence, the correct answer is option: 'A'.