The diagram shows a lamina that consists of a uniform semicircular plate of radius a attached to

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The diagram shows a lamina that consists of a uniform semicircular plate of radius a attached to a uniform rectangular plate of dimensions a and 2a.

The density of the rectangular section is twice the density of the semicircular section.

a. Find the centre of mass of the combined lamina from the edges AB and BC.

b. The lamina is suspended from the point A and allowed to hang in equilibrium. Find the angle between AB and the vertical.

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