Question

A lamina occupies the part of the disk x2 + y2 ≤ 49 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis. (x, y) =

Answer 1

Answer:

xcm = 21/4

ycm = 21/4

Step-by-step explanation:

The region of integration (part of the disk x ² +y² ≤ 49 in the first quadrant) is

described easily in polar coordinates as the set of all (r, θ) with 0 ≤ r ≤ 7 and 0 ≤ θ ≤  π /2 .

Also, the density is ρ(x, y) = k*y = k*r*Sin θ , where k is a constant of  proportionality.

We can see the solution in the pic shown.