Question

Moment of Inertia of a body depends on
A.) Axis of rotation
B.) Torque
C.) Angular Momentum
D.) Angular velocity

Answer 1

Hint: Moment of Inertia is a rotational analogue for mass. The moment of inertia is proportional and depends upon the mass distribution, axis of rotation and the shape of the object. It has different values for bodies of different shape and density.

Complete step by step answer:

The moment of inertia is a quantity that determines the amount of torque needed to get a desired amount of angular acceleration. The moment of inertia of a particle of mass $m$ which is rotating around the axis at a distance r from the axis is given by, $I=m{{r}^{2}}$.
For a body having continuous mass distribution, the moment of inertia can be written as,

$I=\int{{{r}^{2}}dm}$

Where, dm is the small mass element we are considering in the body at a distance r from the axis.
So, as you can see from the equation the moment of inertia of a body depends on both its mass distribution and the distance from the axis.
The moment of inertia for the same body differs if we are considering different axes about which the body is rotating.

Also, Moment of inertia varies with the shape of the object.

So the answer to the question is option (A)- Axis of rotation.

Note: The torque which is defined in the options is the product of the moment of inertia of the body and the angular acceleration of the body. Torque is a vector quantity. It can be written mathematically as,

\[\text{Torque }\left( \overrightarrow{\tau } \right)=I\overrightarrow{\alpha }\], where, $\overrightarrow{\alpha }$ is the angular acceleration.

The angular momentum which is defined in the options is the product of the moment of inertia of the body and the angular velocity of the body. Angular velocity and angular momentum are vector quantities. It can be written mathematically as,
$\text{Angular Momentum }\left( \overrightarrow{L} \right)=I\overrightarrow{\omega }$, where, $\overrightarrow{\omega }$ is the angular velocity of the body.