Question

A light rope is wound around a hollow cylinder of mass $4\, kg$ and radius $40\, cm.$ If the rope is pulled with a force of $40\, N.$ it's angular acceleration is

• A. $0.40 \, rads^{-2}$
• B. $0.25 \, rads^{-2}$
• C. $25 \, rads^{-2}$
• D. $40 \, rads^{-2}$

Answer 1

Answer: (C)

Torque, $\tau=I \alpha$
$F \times r =M r^{2} \alpha$
$40 \times 0.4=4 \times(0.4)^{2} \alpha$
$16=0.64 \alpha$
$\alpha=\frac{16}{0.64}$
$=\frac{16}{64} \times 100$
$=25\, rad / s ^{2}$