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  4. A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is angular acceleration (in rad / s 2 ) of the cylinder if the rope is pulled with a force of 30 N ? Assume that there is no slipping.

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Q. A rope of negligible mass is wound round a hollow cylinder of mass $3\, kg$ and radius $40 \,cm$. What is angular acceleration (in $rad / s ^{2}$ ) of the cylinder if the rope is pulled with a force of $30\, N$ ? Assume that there is no slipping.

System of Particles and Rotational Motion

Solution:

Here $M=3\, kg , R=40\, cm =0.40 \, m , F=30 \, N$
Torque, $\tau=F \times R=30 \times 0.40=12 \, Nm$
M.I. of the hollow cylinder about it own axis,
$I=M R^{2}=3 \times(0.40)^{2}=0.48 \, kg \, m ^{2}$
Angular acceleration,
$\alpha=\frac{\tau}{I}=\frac{12}{0.48}=25\, rad\, s ^{-2}$