Question

The moment of inertia of a body is independent of

• A. Mass of the body
• B. Position of axis
• C. Nature of distribution of mass about axis of rotation
• D. Angular velocity

Answer 1

The correct option is D

Angular velocity

Explanation of correct option:

In Case of Option D:

1. Moment of inertia of a body is given as, $I=m{r}^2$ (where, $m$ mass of the body and $r$ is the distance of the body from the axis of rotation).
2. Moment of inertia of a body depends only on $m$ and $r$ , so it does not depend on angular velocity.
3. Therefore moment of inertia is independent of angular velocity.

Explanation of incorrect options

In case of option A

1. It is clear from the equation that moment of inertia depends on mass of the body.
2. Thus option A is incorrect

In case of option B

1. If we observe the figure, we can say that moment of inertia of the body about y-axis is not the same as the moment of inertia of the body about x-axis, therefore the moment of inertia depends on position of axis.
2. Thus option B is incorrect

In case of option C

1. As the distribution of mass varies the distance r from the axis of the body, change in nature of distribution of mass about axis of rotation affects the moment of inertia of the body. Therefore, moment of inertia depends on nature of distribution of mass about axis of rotation.
2. Thus option B is incorrect

Hence, option (D) is correct.