Question

A solid cylinder of mass $50$ $kg$ and radius $0.5$ $m$ is free to rotate about the axis passing through its centre. 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 $2rad{s}^{-2}$ is

• A. $78.5$ $N$
• B. $157$ $N$
• C. $25$ $N$
• D. $50$ $N$

Answer 1

The correct option is C $25$ $N$

Let, the tension produced in the string be $T$.
Then, the torque due to the tension $T$ about the centre of the cylinder of radius $R$ is given by,

$\tau =T$×$R$
where, $\tau =I\alpha =\frac{1}{2}M{R}^2\times \alpha$
(Since moment of inertia of cylinder about the axis passing through its centre, $I=\frac{1}{2}M{R}^2$)
$T\times R=\frac{1}{2}M{R}^2\times \alpha$

$T=\frac{1}{2}MR\times \alpha$

$T=\frac{1}{2}\times 50\times 0.5\times 2=25$ N.