A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Fig. 7.3). The moment of inertia about the z-axis is then
C. the same
D. changed in unpredicted manner
As the piece Q is removed and glued to centre, the moment of inertia decreases about z-axis as the
As the distance of that piece from z-axis is decreased to zero, hence its M.I will decrease. Hence, correct option is b.
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(Hint: Square of the distance of a point (x, y) in the x–y plane from an axis through the origin and perpendicular to the plane is x2 + y2).
B. Prove the theorem of parallel axes.
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