For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O ' (corner point) is:

Step-by-step solution

We will use Parallel Axes Theorem here, Distance between O O ' is, O O ' = 1 2 a 2 + b 2 = a 2 4 + b 2 4 So, according to parallel axis theorem we have, I O I O ' = M 12 a 2 + b 2 M 12 a 2 + b 2 + M a 2 4 + b 2 4 = M 12 a 2 + b 2 M 3 a 2 + b 2 = 1 4