A uniform rod AB of length l and mass M hangs from point A at which it is freely hinged in a car moving with velocity v₀. The rod can rotate in vertical plane about the axis at A. If the car suddenly stops

Question

G1 Physics · Accepted Answer

The car stops impulsively, but the rod retains linear momentum. Conserving angular momentum about hinge A during the impulse gives ω=3v₀/(2ℓ). Comparing rotational energy after impact with the initial translational energy gives an energy loss Mv₀²/8. The minimum speed for a complete loop follows from energy, v₀(min)=√(8gℓ/3). Thus A,B,C.