Two identical rods are joined to form an ‘X’. The smaller angle between the rods is ‘ $θ$ ’. The moment of inertia of the system about an axis passing through the point of intersection of the rods and perpendicular to their plane is

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$α θ$

$α \sin^{2} θ$

$α \cos^{2} θ$

independent of $θ$

answer is D.

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Detailed Solution

Regardless of the angle between them, the moment of inertia of the two rods will always be the sum of their individual moment of inertias.

$I_{total} = I_{A} + I_{B}$

$I_{total} = \frac{{ml}^{2}}{12} + \frac{{ml}^{2}}{12}$

Hence the correct answer is independent of θ.

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