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 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 ( $g=10 \, m \, s^{- 2}$ )
Updated On: Jul 2, 2022
- $2kgm^{2}$
- $1 \, kg \, m^{2}$
- $4 \, kg \, m^{2}$
- $8 \, kg \, m^{2}$
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The Correct Option is A
Solution and Explanation
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 $I=2\text{kg m}^{2}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.