Question

Name the factor on which the moment of inertia of a body depends.
This question has multiple correct options
A. Mass
B. Force
C. Distance from the rotating axis
D. Density

Answer 1

Hint: You can start by defining the moment of inertia clearly explaining what factors affect it. Then write down the equation for the moment of inertia of a particle, i.e $I = m{r^2}$ , and then for a body, i.e $I = \mathop \sum \limits_i {m_i}r_i^2 = {m_1}r_1^2 + {m_2}r_2^2 + {m_3}r_3^2 + ...$ . Then use equations to further clarify how the moment of inertia depends on mass and distance from the rotating axis.

Complete step by step answer:
Moment of inertia - It is also called mass moment of inertia or the rotational inertia of a body. Moment of inertia is the sum of the products of mass of each particle with the square of the distance of each particle from the axis of rotation. Moment of inertia is based on the concept of the center of mass. The center of mass is an imaginary point in a body where all the mass of the body can be considered to be collected.
The equation for the moment of inertia of a particle is
$I = m{r^2}$
For a whole body
$I = \mathop \sum \limits_i {m_i}r_i^2 = {m_1}r_1^2 + {m_2}r_2^2 + {m_3}r_3^2 + ...$
From the above equation, we learn some crucial points. In simple words the moment of inertia of a body depends on the body’s mass distribution and distance from the axis of rotation.
The moment of inertia of a body is directly proportional to its mass and the distance of the particles of the body from the axis of rotation.
Hence, the moment of inertia depends on mass and distance from the rotating axis, and force and density do not affect the moment of inertia of a body.
Hence, options A and C are the correct options.

Note: The concept of center of mass is very crucial for calculating the moment of inertia. The concept of center of mass is very interesting. We know that for calculating the electrostatic and gravitational force exerted by a body we also consider them as a point charge and point mass respectively. Essentially we consider all the charges and the mass to be concentrated at the center. Remember this charge or mass is always considered to be inside the body, but in the case of the center of mass it can also be situated outside of the body, for example – The center of the mass of a Banana.