A symmetric lamina of mass M consists of a square shape with a semicircular section over of the edge of the square as shown in fig. p-10. The side of the square is 2a. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is `1.6Ma^2`. The moment of inertia of the lamina is ......
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Assuming symmetric lamina to in xy plane, we will have `I_x = l_y` (Since the mass distributon is same about x-axis and y-axis `I_x+I_y = I_z` (perpendicular axis theorem) it is given that `I_z = 1.6 Ma^2` Hence `I_x = I_y = (I_z)/(2) =0.8 Ma^2` Now, according to parallel axis theorem, we get `I_(AB) = I_x + M(2a)^2` `= 0.8 Ma^2 + 4Ma^2` `=4.8Ma^2` M
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