A rope is wound around a solid cylinder of mass $1 \mathrm{~kg}$ and radius $0 \cdot 4 \mathrm{~m}$. What is…

A rope is wound around a solid cylinder of mass $1 \mathrm{~kg}$ and radius $0 \cdot 4 \mathrm{~m}$. What is the angular acceleration of cylinder, if the rope is pulled with a force of $25 \mathrm{~N} ?$ (cylinder is rotating about its own axis)
  1. $50 \mathrm{rad} / \mathrm{s}^{2}$
  2. $125 \mathrm{rad} / \mathrm{s}^{2}$
  3. $10 \mathrm{rad} / \mathrm{s}^{2}$
  4. $1 \mathrm{rad} / \mathrm{s}^{2}$

Solution

Torque $\tau=F r=25 \times 0.4=10 \mathrm{Nm}$ $\begin{array}{l}I=\frac{M R^{2}}{2}=\frac{1 \times(0.4)^{2}}{2}=0.08 \mathrm{~kg}-\mathrm{m}^{2} \\ \alpha=\frac{\tau}{I}=\frac{10}{0.08}=125 \mathrm{rad} / \mathrm{s}^{2}\end{array}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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