Question

PII
33)
Two identical uniform rod each of mass. m and length
I joined perpendicular to each other. An axis passes
through junction and in the plane of rods. Then M.I.
of system about the axis is
45°
09
way mo?
(3) m12​

Answer 1

The basic relationship between MI of rod at an angle of $\theta$ with axis is given as :

$MI = \dfrac{1}{3} m {l}^{2} { \cos}^{2} (\theta)$

So total MI will be sum of Moment Of Inertia of individual rods . Upper rod is making an angle 45° with axis , while lower rod is making angle of 135° with axis.

Total Moment Of Inertia

$= \dfrac{1}{3} m {l}^{2} { \cos}^{2} (45 \degree) + \dfrac{1}{3} m {l}^{2} { \cos}^{2} (135 \degree)$

$= \dfrac{1}{3} m {l}^{2} {( \dfrac{1}{ \sqrt{2} }) }^{2} + \dfrac{1}{3} m {l}^{2} {( \dfrac{-1}{ \sqrt{2} }) }^{2}$

$= \dfrac{1}{6} m {l}^{2} + \dfrac{1}{6} m {l}^{2}$

$= \dfrac{1}{3} m {l}^{2}$

So total Moment Of Inertia will be ⅓ml²

So correct Option is Option 1)

Answer 2

Answer:

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