Two particles of mass m move with equal speed v₀ in opposite directions and strike the ends of a rigid massless rod of length ℓ perpendicular to the rod. They stick to the rod. What is the tension in the rod during the subsequent rotation?

Question

G1 Physics · Accepted Answer

The two particles stick to the ends, so the final centre of mass is at rest because initial linear momentum is zero. Initial angular momentum about the rod centre is initial L=2[mv₀(ℓ/2)]=mv₀ℓ. Final inertia is I=2m(ℓ/2)²=mℓ²/2, so ω=2v₀/ℓ. Each particle needs centripetal force T=mω²(ℓ/2)=2mv₀²/ℓ. Hence option A.