Question

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 $2$ revolutions $s^{-2}$ is

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

Answer 1

Answer: (D)

Here, mass of the cylinder, $M=50kg$
Radius of the cylinder, $R=0.5m$
Angular acceleration, $\alpha =2\text{rev}{s}^{-2}$
$2\times 2\pi rad{s}^{-2}=4\pi rad{s}^{-2}$
Torque, $\tau =TR$
Moment of inertia of the solid cylinder about its axis, $I=\frac{1}{2}M{R}^2$
$\therefore$ Angular acceleration of the cylinder
$\alpha =\frac{\tau }{1}=\frac{TR}{\frac{1}{2}M{R}^2}$
$T=\frac{MR\alpha }{2}=\frac{50\times 0.5\times 4\pi }{2}=157N$