Two plates made of the same material and thickness are joined as shown. One plate is circular and another square in shape. The diameter of circular plate is equal to the side of the square plane. Locate `c.m.`

Explanation

The diagram is symmetrical about the `x`-axis.
`Mass prop area`
Square plate : `m_(1) prop d^(2) rArr m_(1) = kd^(2) , x_(1) = (d)/(2)`
Circulare plate : `m_(2) prop pi(d//2)^(2)`
`m_(2) = k(pi d^(2))/(4) , x_(2) = d + (d)/(2) = (3d)/(2)`
`x_(m) = (m_(1) x_(1) + m_(2) x_(2))/(m_(1) + m_(2)) = (kd^(2) xx (d)/(2) + (k pi d^(2))/(4) xx (3d)/(2))/(kd^(2) + (k pi d^(2))/(4))`
`((d)/(2) + (pi)/(4) xx (3d)/(2))/(1 + (pi)/(4)) = ((d( 4 + 3pi))/(8))/((4 + pi)/(4))`
`= ((3 pi + 4)d)/(( 2pi + 8)) = 0.94 d`
It may be noted , since `m_(1) gt m_(2) , c.m.` will lie in square the plate.