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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s⁻² is:

1. 25 N
2. 50 N
3. 78.5 N
4. 157 N

Correct answer: 78.5 N

Solution

The angular acceleration is given as 2 revolutions/s², which is converted to radians/s² as 2 × 2π = 4π rad/s². The moment of inertia of the solid cylinder about its axis is I = (1/2)MR². Torque τ = Iα, and τ = T × R. Solving for T, we get T = (Iα)/R = [(1/2)(50)(0.5²)(4π)] / 0.5 = 78.5 N.

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