Question

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

• A. $2kgm^{2}$
• B. $1 \, kg \, m^{2}$
• C. $4 \, kg \, m^{2}$
• D. $8 \, kg \, m^{2}$

Answer 1

Answer: (A)

$2kgm^{2}$

Answer 2

Given, $r=0.4m$ , $\alpha = 8 \text{ rad } \text{s}^{- 2}$ $m=4kg$ , $I=?$ Torque, $\tau=I\alpha$ $\Rightarrow \textit{mgr}=\textit{I}\alpha$ or $4 \times 1 0 \times \text{0.4} = \text{I} \times 8$ $\Rightarrow$ $I=\frac{16}{8}=2kgm^{2}$ Or $I=2\text{kg m}^{2}$