Question

A rope is wound round a hollow cylinder of mass $5 \,kg$ and radius $60\, cm$. If the rope is pulled with a force of $80\, N$. What is the angular acceleration of the cylinder?

• A. $25\, rad / s ^{2}$
• B. $26.6 rad / s ^{2}$
• C. $30 rad / s ^{2}$
• D. $38 rad / s ^{2}$

Answer 1

Answer: (B)

$I=M R^{2}=5 \times(0.6)^{2}=5 \times 0.36=1.8\, kg \,m ^{2}$
Torque $=80 \times 0.6=48\, Nm$
$\tau=I \alpha$
$\therefore \alpha=\frac{\tau}{I}=\frac{48}{1.8}$
$=26.6 \,rad \,s ^{-2}$