# Collision Fun!!

A uniform smooth rod of mass $$M = 2.5 \text{ kg}$$ and length $$l = 4 \text{ m}$$ is lying still on a smooth horizontal table. Now I shoot a small ball of mass $$m = 2 \text{ kg}$$ from point $$P$$ such that it traces the path shown and hit the rod at a distance of $$l / 4$$ from the centre. The ball collides elastically with the rod. Let $$\omega$$ represents the angular velocity of the rod just after collision and $${v}_\text{rel}$$ represents the relative velocity of ball just after collision with respect to centre of mass of the rod.

Find $${v^2}_\text{rel} \times \omega$$.

Details and Assumptions:

• The ball was given an impulse $$I = 20 \text{ kg m/s}$$ at point $$P$$.
• Consider the figure for geometry.
• Friction is absent everywhere.
• The rod is completely free (that is free to do translational as well as rotational motion).

This is Original

×