Question

The moment of inertia of a rigid body, depends upon:

• A. distribution of mass from axis of rotation
• B. angular velocity of the body
• C. angular acceleration of the body
• D. mass of the body

Answer 1

Answer: (A)

Let there be a rigid body of mass $M$. Let the body be made up of a large number of minute particles with masses $m_1,m_2,m_3,\dots \dots \dots$, and $r_1,r_2,r_3,\dots$ be their respective distances from the axis of rotation.
Then their moments of inertia are
$m_1{r}_1^2,m_2{r}_2^2,m_3{r}_3^2,\dots \dots$

The moment of inertia of the whole body about the axis of rotation will be
$I=m_1{r}_1^2+m_2{r}_2^2+m_3{r}_3^3+\dots \dots$
or $I=\Sigma m{r}^2$
Hence, moment of inertia depends upon the distribution of mass from axis of rotation.