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A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is:

1. 2 × 10⁻⁶ Nm
2. 2 × 10⁻³ Nm
3. 12 × 10⁻⁴ Nm
4. 2 × 10⁶ Nm

Correct answer: 2 × 10⁻³ Nm

Solution

The moment of inertia of the solid cylinder about its axis is I = (1/2)MR². The angular velocity ω is converted from rpm to rad/s. Using the work-energy principle, the work done by the torque equals the initial rotational kinetic energy. Torque is then calculated using the angular displacement (2π revolutions).

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