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A solid cylinder of mass 50kg and radius 0.5m 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 rad s² is

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50N

157N

78.5N

25N

answer is D.

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Detailed Solution

We know that,

$I_{Cylinder} = \frac{{MR}^{2}}{2} = \frac{50 \times {(\frac{1}{2})}^{2}}{2} = \frac{50}{8} {kgm}^{2}$

Also torque due to tension = TR = $Iα$

$TR = (\frac{50}{8}) \times 2 \Rightarrow T \times \frac{1}{2} = \frac{50}{4}$

$\Rightarrow T = 25 N$

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