Physics - Center of Mass Question with Solution | TestHub

For a perfectly inelastic collision, the particles stick together and move as a single system. Momentum is conserved.

Initial momentum of the system: The particle of mass $m$ has momentum $mv$. The rod of mass $2m$ is stationary, so its momentum is $0$. Total initial momentum $P_i=mv$.

After the perfectly inelastic collision, the combined mass is $M_{total}=m+2m=3m$. Let the velocity of the center of mass of the combined system be $V_{CM}$. Total final momentum $P_f=(3m)V_{CM}$. By conservation of momentum: $P_i=P_f$.$$mv=(3m)V_{CM}$$ $$V_{CM}=\frac{mv}{3m}=\frac{v}{3}$$ The velocity of the center of mass of the combined system immediately after the collision is $v/3$.