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## Homework Statement

A thin rod AB of mass ##m_{1}## and of length ##l## is placed on a smooth horizontal ground. A point sized particle of mass ##m_{2}## having a velocity ##v## making an angle ##\theta##with the line perpendicular to ##AB## collides with the rod at point ##A##.

Assuming the collision to be elastic find ##\theta## such that the point sized particle again collides with the rod at point ##B##.

## Homework Equations

## The Attempt at a Solution

T[/B]he image was provided with the question.

When two things collide equal and opposite impulses acts along the direction perpendicular to the contact surface. So in this situation if the particle collides with rod at point A then the impulse which acts on the rod passes through the CoM of the rod. So no impulsive torque acts on the rod about its CoM. So the rod will not rotate. And without rotating, it is not possible for the particle to collide again at point B.

So, how this can be solved?