Question

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