Find the position of centre of mass of the uniform lamina shown in figure.

Explanation

Hence,
`A_(1)=` area of complete circle `=pia^(2)`
`A_(2)=` area of small circle `=pi((a)/(2))^(2)=(pi a^(2))/(4)`
` (x_(1), y_(1)) =` coordinates of centre of mass of large circle `= (0, 0)` and `(x_(2), y_(2)) =` coordinates of centre of mass of small circle `=((a)/(2),0)`
Using `x_(COM)=(A_(1)x_(1)-A_(2)x_(2))/(A_(1)-A_(2))`
we get `x_(COM)= (-(pia^(2))/(4)((a)/(2)))/(pia^(2)-(pia^(2))/(4))=(-((1)/(8)))/(((3)/(4)))a=-(a)/(6)`
and `y_(COM)=0` as `y_(1) and y_(2)` both are zero.
Therefore, coordinates of COM of the lamina shown in figure are `(-(a)/(6),0)`