JEE Advanced 2023 Physics question

A bar of mass kg and length 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 kg is moving on the same horizontal surface with speed on a path perpendicular to the bar. It hits the bar at a distance 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 . Which of the following statement is correct?

• (A) and v Correct
• (B) and v
• (C) and v
• (D) and v