One half of a uniform circular disk of radius 1 lies with its diameter along the y axis and the center of the origin. the mass of the half-disk is 1. find the location of center of mass.

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 Let (a,b) be the coordinates of the mass center. 

By symmetry, b = 0. 

To get a, consider x^2+y^2 = R^2 in the first quadrant, 
a 
= (4/ piR^2) ∫x sqrt(R^2 - x^2)dx, from 0 to R 
= (4/ piR^2)(1/2)(2/3)(R^2)^(3/2) 
= 4R/(3pi)

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