Three uniform rods each of mass m and length l are arranged as the three sides of triangle lies on a plane. Find moment of inertia about an axis passing through any vertices and perpendicular to plane.
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The moment of inertia about an axis passing through any vertices and perpendicular to plane = 3Ml²/2
The rods are joined in the form of a triangle(equilateral triangle).
When we see the moment of inertia through a vertex perpendicular to the plane , two of the rods will have momentum of inertia equal to the inertia through the end of rods .
For the third rod we will use parallel axis theorem to find the moment of inertia .
Moment of inertia = Ml²/3 + Ml²/3 + (Ml²/3 + M(√3l/2)²)
=> 2Ml²/3 + 5Ml²/6
=> 9Ml²/6
=> 3Ml²/2
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