JEE Physics Practice Question

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 $L / 2$ from the pivoted end and returns back on the same path with speed $\mathrm{v}$. After this elastic collision, the bar rotates with an angular velocity $\omega$. Which of the following statement is correct?

1. A.$\omega=6.98 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
2. B.$\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
3. C.$\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=10.0 \mathrm{~m} \mathrm{~s}^{-1}$
4. D.$\omega=6.80 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.10 \mathrm{~m} \mathrm{~s}^{-1}$