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A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

1. 0.25 rad/s²
2. 25 rad/s²
3. 5 m/s²
4. 25 m/s²

Correct answer: 25 rad/s²

Solution

The torque on the hollow cylinder is given by τ = F × r, where F = 30 N and r = 0.4 m. The moment of inertia of a hollow cylinder is I = m × r², where m = 3 kg and r = 0.4 m. Using the relation τ = I × α, we find α = τ / I = (30 × 0.4) / (3 × 0.4²) = 25 rad/s².

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