A bar of mass \( M = 1.00 \, \text{kg} \) and length \( L = 0.20 \, \text{m} \) 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 \( m = 0.10 \, \text{kg} \) is moving on the same horizontal surface with \( 5.00 \, \text{m s}^{-1} \) 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 statement is correct?
