Question

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

• A. If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
• B. If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
• C. If the Assertion is correct but Reason is incorrect.
• D. If the Assertion is incorrect and Reason is correct.

Answer 1

Answer: (B)

We know that
$I=\frac{m_1{r}_1{}^2+m_2{r}_2{}^2+m_3{r}_3{}^3+\dots ..+m_n{r}_n{}^2}{m_1+m_2+m_3+\dots ..}$
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 I depends upon distribution of the masses and position of axis.
So, Assertion is correct.
We know that,
angular momentum $=I\omega$
Torque $=$ I $\alpha$
If we compare these equations with equations like linear momentum $=mv$, force $=m$, we find that I represents mass in angular motion.