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Problem 11 Easy Difficulty

Polar moment of inertia of an elliptical plate $A$ thin plate of constant density covers the region bounded by the ellipse $x^{2} / a^{2}+y^{2} / b^{2}=1, a>0, b>0,$ in the $x y$ -plane. Find the first
moment of the plate about the origin. (Hint: Use the transformation $x=a r \cos \theta, y=b r \sin \theta . )$

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