A bar of mass $M=1.00 \mathrm{~kg}$ and length $\mathrm{L}=0.20 \mathrm{~m}$ 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 $\mathrm{m}=0.10 \mathrm{~kg}$ 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 $\mathrm{L} / 2$ 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?
Select the correct option:
A
$\omega=6.98 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
B
$\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
C
$\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=10.0 \mathrm{~m} \mathrm{~s}^{-1}$
D
$\omega=6.80 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.10 \mathrm{~m} \mathrm{~s}^{-1}$
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