A uniform rod AB of length L and mass m hangs vertically from a hinge at A. A particle of mass m moving horizontally with speed v strikes the midpoint and comes to rest. What is the magnitude of the impulsive reaction at hinge A?

Question

G1 Physics · Accepted Answer

During the impact, angular momentum about hinge A is conserved: mv(L/2)=Iₐω, where Iₐ=mL²/3 for the rod. Thus ω=3v/(2L). Linear impulse on the rod is mV of CM with V of CM=ωL/2=3v/4, so the hinge impulse equals the difference between the rod’s momentum and the particle impulse: Jₐ=3mv/4-mv=-mv/4. Magnitude =mv/4. Hence option D.