Question

A thin wire has the shape of the quarter circle in the first quadrant. The circle is centered at the origin with radius a. Let rho = kxy be the linear density of the wire. Here k > 0 is just a constant. Find the mass and the center of mass of the wire

Answer 1

mass =
`(k*a^(3) )/(2)`

COM of arc (
`(2a)/(3)`,
`(2a)/(3)`)

Step-by-step explanation:

By using cylendrical coordinate system find total mass and COM position.

This arc is symmetric about x=y thus COM lies on this line.

Rest is in attachment.