The moment of inertia of a system of four rods, each of length l and mass m, about the axis shown is

Question

The moment of inertia of a system of four rods, each of length l and mass m, about the axis shown is (A) (2/3) m l2 (B) 2 m l2 (C) 3 m l2 (D) (8/3) m l2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/5ec2917c0b3a5c384a08c821c3d619ad-.png" /> Moment of inertia about 2: I2=4((m l2/3) sin 2 45°)=(2 m l2/3) Apply perpendicular axis theorem, I1 =I2+m h2 =(2 m l2/3)+4 m((1/√2))2=(8/3) m l2

Q. The moment of inertia of a system of four rods, each of length $l$ and mass $m$ , about the axis shown is

$\frac{2}{3} m l^{2}$

$2 m l^{2}$

$3 m l^{2}$

$\frac{8}{3} m l^{2}$

Moment of inertia about $2 :$
$I_{2} = 4 (\frac{m l ^{2}}{3} sin^{2} 4 5^{\circ}) = \frac{2 m l ^{2}}{3}$
Apply perpendicular axis theorem,
$I_{1} = I_{2} + m h^{2}$
$= \frac{2 m l ^{2}}{3} + 4 m (\frac{1}{2})^{2} = \frac{8}{3} m l^{2}$

Q. The moment of inertia of a system of four rods, each of length l and mass m, about the axis shown is

32​ml2

2ml2

3ml2

38​ml2