Question

Moment of inertia of the object depends upon
A. Mass of body
B. Axis of rotation of the body
C. Shape and size of body
D. All of the above

Answer 1

Hint: The moment of inertia of the body is the additional property of the object. The moment of inertia of the body can be calculated using the formula:
\[I=\sum m_{i}r_{i}^{2}\]

Complete step-by-step answer:
Moment of inertia is also known as the rotational inertia. When masses are in linear motion, its rotational analog is known as rotational inertia. The moment of inertia provides the relationship for dynamics of rotational motion. The moment of inertia can be calculated with respect to the axis of rotation of the particles.
Thus, moment of inertia in other terms is known as the mass distribution of the particle with respect to the axis of rotation. The distribution of the particle from the axis of rotation is also dependent on the shape and size of the object. Thus, the moment of inertia of the object depends on the mass, axis of rotation and shape and size of the body.
Option (D) is correct.

Note: Alternate method
Considering the object consists of n number of particles, the distance of each particle is r from its axis of rotation. The formula of the moment of inertia can be given as:
\[I=\sum m_{n}r_{n}^{2}\]
Where, $m_{n}$ is the mass of each particle of the object and $r_{n}$ is the distance of the particle from the axis of rotation.
The distance of each particle from the axis of rotation is dependent on the shape and size of the object.
Therefore,
\[I \propto m\]
\[I \propto r^{2}\]
Thus, the moment of inertia of the object depends on the mass, axis of rotation and shape and size of the body.