Question

A solid cylinder of mass $50\text{kg}$ and radius $0.5\text{m}$ 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 $2{\text{rev/s}}^2$ is

• A. $25\text{N}$
• B. $50\text{N}$
• C. $8.5\text{N}$
• D. $157\text{N}$

Answer 1

The correct option is D $157\text{N}$

$M=50kg$
$R=0.5m$
$\alpha =2\mathrm{rev}/s^2=4\pi \mathrm{rad}/s^2$
Torque, $\tau =R\times T=I\alpha$
$⟹T\times R=\frac{M{R}^2}{2}\times 4\pi$
$\begin{array}{cc}T& =MR\times 2\pi \\ & =50\times \frac{1}{2}\times 2\pi \\ T=& 50\pi =50\times 3.14=157N\end{array}$