Question

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m, moving at a speed v, perpendicular to the length of the rod strikes it at a distance $\frac{a}{4}$ from the center and stops after the collision. The angular velocity of the rod about its center just after the collision is-

• A. $\frac{3mv}{Ma}$
• B. $\frac{mv}{Ma}$
• C. $\frac{2mv}{3Ma}$
• D. $0$

Answer 1

The correct option is A $\frac{3mv}{Ma}$


Taking Angular Momentum about the centre of mass C of the rod.
$mv\frac{a}{4}=\frac{1}{12}M{a}^2\omega \Rightarrow \omega =\frac{3mv}{MA}$