A disc of radius $0.4 \mathrm{~m}$ and mass $1 \mathrm{~kg}$ rotates about an axis passing through its…

A disc of radius $0.4 \mathrm{~m}$ and mass $1 \mathrm{~kg}$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration of the disc is $10 \mathrm{rad} / \mathrm{s}^2$. The tangential force applied to the rim of the disc is
  1. $4 \mathrm{~N}$
  2. $1 \mathrm{~N}$
  3. $2 \mathrm{~N}$
  4. $8 \mathrm{~N}$

Solution

$\mathrm{R}=0.4 \mathrm{~m}, \mathrm{M}=1 \mathrm{~kg}, \alpha=10 \mathrm{rad} / \mathrm{s}^2$ Moment of inertia, $\mathrm{I}=\frac{\mathrm{MR}^2}{2}=\frac{1 \times(0.4)^2}{2}=0.08 \mathrm{~kg} \mathrm{~m}^2$ Torque, $\tau=\mathrm{RF}=\mathrm{I} \alpha$ $\therefore \mathrm{F}=\frac{\mathrm{I} \alpha}{\mathrm{R}}=\frac{0.08 \times 10}{0.4}=2 \mathrm{~N}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

Practice more Rotational Motion questions on Aicharya