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A solid cylinder of mass $\mathbf{5 0} \mathrm{kg}$ and radius $0.5 \mathrm{~m}$ is free to rotate about the horizontal axis. 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 $\mathbf{S}^{-2}$ is :-Option A $\quad 25 \mathrm{~N}$Option B $\quad 50 \mathrm{~N}$Option C $\quad 78.5 \mathrm{~N}$Option D $\quad 157 \mathrm{~N}$
A solid cylinder of mass $\mathbf{5 0} \mathrm{kg}$ and radius $0.5 \mathrm{~m}$ is free to rotate about the horizontal axis. 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 $\mathbf{S}^{-2}$ is :-
Option A $\quad 25 \mathrm{~N}$
Option B $\quad 50 \mathrm{~N}$
Option C $\quad 78.5 \mathrm{~N}$
Option D $\quad 157 \mathrm{~N}$
Physics
A solid cylinder of mass $\mathbf{5 0} \mathrm{kg}$ and radius $0.5 \mathrm{~m}$ is free to rotate about the horizontal axis. 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 $\mathbf{S}^{-2}$ is :-
Option A $\quad 25 \mathrm{~N}$
Option B $\quad 50 \mathrm{~N}$
Option C $\quad 78.5 \mathrm{~N}$
Option D $\quad 157 \mathrm{~N}$

The correct option is D

$\alpha=2$ revolution $/ \mathrm{s}^{2}=4 \pi \mathrm{rad} / \mathrm{s}^{2}$

$\mathrm{I}=\frac{1}{2} \mathrm{MR}^{2}$

As $\tau=I \alpha$ so $T R=I \alpha$

$\mathrm{TR}=\mathrm{I} \alpha$

$\mathrm{TR}=\frac{\mathrm{MR}^{2}}{2} \alpha$

$\mathrm{T}=\frac{\mathrm{MR}}{2} \alpha$

$\Rightarrow \mathrm{T}=\frac{\mathrm{I} \alpha}{\mathrm{R}}=\frac{50 \times 0.5 \times(4 \pi)}{2} \mathrm{~N}$

$=50 \pi \mathrm{N}=157 \mathrm{~N}$

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