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Rotational Motion

Section: Physics

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Question : 8 of 24

Marks: +1, -0

Three thin uniform rods each of mass M and length L are placed along the three axes of a cartesian coordinate system with one end of all the rods at origin. The moment of inertia of the system of the rods about z-axis is

[AP EAPCET 22 May 2025 S1]

$\;\frac{(ML)^2}{3}$
$\;\frac{2 (ML)^2}{3}$
$\;\frac{(ML)^2}{2}$
$(ML)^2$

Solution:

The moment of inertia of a rod about an axis perpendicular to the rod and passing through one end is

\;\frac{M L^2}{3}

. Two rods are in the

X

and

Y

-axis and they both contribute to the moment of inertia about the

Z

-axis. The rod along

the

Z

-axis does not contribute to the moment of inertia about the

Z

-axis. Therefore the total moment of inertia of the system is

\;\frac{M L^2}{3} + \;\frac{M L^2}{3} = \;\frac{2 M L^2}{3}

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