Question

Assertion :Moment of inertia depends on the axis of rotation and the nature of distribution of the mass of the body. Reason: Moment of inertia is the rotational inertia of the body.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

We know that
$I=\frac{m_1{r}_1^2+m_2{r}_2^2+m_3{r}_3^3+....+m_n{r}_n^2}{m_1+m_2+m_3+......}$
where $r_1,r_2,r_3$ are distances of mass $m_1,m_2,m_3$ etc. from the axis. From the relation it is clear that it depends upon distribution of the masses and position of axis.
So, assertion is true.
We know that
angular momentum $=I\omega$
$Torque=I\alpha$
If we compare these equations with equations like linear momentum $=mv,force=ma$, we find that I represents mass in angular motion. As mass represents inertia in linear motion, I represents inertia in angular motion.
But assertion and reason are mutually exclusive. So (b) is the answer.