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Given, mass of cylinder m = 3 kg, R = 40 cm = 0.4 m, F = 30 N. Find angular acceleration α.

1. α = 10 rad/s²
2. α = 25 rad/s²
3. α = 5 rad/s²
4. α = 15 rad/s²

Correct answer: α = 10 rad/s²

Solution

The torque τ is given by τ = F × R. Using τ = I × α, where I for a solid cylinder is (1/2)mR², we solve for α: α = τ/I = (F × R) / ((1/2)mR²). Substituting F = 30 N, R = 0.4 m, and m = 3 kg, we get α = (30 × 0.4) / (0.5 × 3 × 0.4²) = 10 rad/s².

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