A rod of mass M and length 2L lies horizontally. A particle of mass m, moving with velocity v in the vertical plane, strikes the end B of the rod and sticks to it. Then the velocity of point B just after collision is:
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In rod–particle sticking collisions, always prefer angular momentum conservation about the system center of mass for clean calculations.
Step 1: Collision description. A particle of mass m strikes the end of a uniform rod (mass M, length 2L) and sticks, constituting a perfectly inelastic collision followed by combined translation and rotation. Step 2: Conservation principle. External impulsive torque about the system's center of mass is negligible during impact, so angular momentum about the CM is conserved. Step 3: Initial angular momentum. Only the particle contributes: L_i = m v L (about rod center). Step 4: Post-collision dynamics. The combined system rotates about its CM with angular velocity ω; total moment of inertia I accounts for rod and particle. Step 5: Angular momentum conservation equation. m v L = I ω → ω = m v L / I. Step 6: Velocity of point B after impact. v_B = ω × distance from CM to B; simplification yields the expression corresponding to Option (3).
