Question

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.

Answer 1

Thank you for posting your question here at brainly. Below are the solution:

 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)

I hope the answer will help