Alamina occupies the part of the disk x2 + y2 ≤ 49 in the first quadrant. find the center of mass of the lamina if the density at any point is proportional to the square of its distance from the origin.

Answer with Explanation:

We are given that a lamina occupies the part of the disk

in the first quadrant.

Radius is a distance between the center of circle and the point on boundary of circle.

By comparing the equation of circle

We have radius =7 and center=(0,0)

Where r= Distance between origin and the point on boundary of circle

Density function

Where K= Proportionality constant

Radius varies from 0 to 7 and  angle() varies from 0 to .

Mass of the lamina=m=

Its first moments is given by

  ()

  ()

 ()

Center of mass is given by

Hence, the center of mass of the lamina=()

a and c

c is 100% but i am confused in a