A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of $8 \mathrm{~rad/s}^{-2}$ is produced in it due to the torque. Then, moment of inertia of the wheel is $\left(g=10 \mathrm{~ms}^{-2}\right)$

• Correct answer
  A

  $2 \mathrm{~kg}-\mathrm{m}^2$
• B

  $1 \mathrm{~kg}-\mathrm{m}^2$
• C

  $4 \mathrm{~kg}-\mathrm{m}^2$
• D

  $8 \mathrm{~kg}-\mathrm{m}^2$

Solution

Given, $\quad r=0.4 \mathrm{~m}$ $\alpha=8 \mathrm{~rad}/ \mathrm{s}^{-1}$ $m=4 \mathrm{~kg}, \quad I=$ ? Torque, $\quad \tau=I \alpha$ $m g r=I \cdot \alpha$ or $\quad 4 \times 10 \times 0.4=I \times 8$ $\Rightarrow \quad I=\frac{16}{8}=2 \mathrm{~kg}-\mathrm{m}^2$ or $I=2 \mathrm{~kg}-\mathrm{m}^2$

Hence, the correct answer is option: 'A'.