A cord of negligible mass is wound around the rim of a wheel supported by spokes of negligible mass. The wheel has mass 10 kg and radius 10 cm and rotates freely without friction. Initially it is at rest. A steady pull of 20 N is applied to the cord. The angular velocity after the cord is unwound by 1 m is:

Question

G1 Physics · Accepted Answer

Because the mass is concentrated at the rim, the wheel has I = MR². Given M=10 kg, R=0.10 m and F=20 N. Torque: τ = FR. Using τ = Iα: FR = MR²α ⇒ α = F/(MR) = 20/[10×0.10] = 20 rad/s². When 1 m of cord is unwound, angular displacement is θ = s/R = 1/0.10 = 10 rad. Starting from rest: ω² = 2αθ = 2×20×10 = 400. Thus ω = 20 rad/s. Correct option: A.