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Answer:
The moment of inertia about an axis through the center and perpendicular to the plane of the square is
Explanation:
From the question we are told that
The length of one side of the square is
The total mass of the square is
Generally the mass of one size of the square is mathematically evaluated as
Generally the moment of inertia of one side of the square is mathematically represented as
Generally given that it means that this moment inertia evaluated above apply to every side of the square
Now substituting for
So
Now according to parallel-axis theorem the moment of inertia of one side of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as
=>
substituting for
=>
=>
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Generally the moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as
=>
=>