Four particles of masses \( 4 \mathrm{~kg}, 2 \mathrm{~kg}, 3 \mathrm{~kg} \) and \( 5 \mathrm{~...

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Four particles of masses \( 4 \mathrm{~kg}, 2 \mathrm{~kg}, 3 \mathrm{~kg} \) and \( 5 \mathrm{~kg} \) are respectively located at the four corners \( A, B \), \( C \), \( D \) of a square of side \( 1 \mathrm{~m} \). Calculate the moment of inertia of the system about the axis passing through point of intersection of the diagonals and perpendicular to the plane of the square
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