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

Answer

A

Explanation

Here, `A_1=` area of complete circle `=pia^2`
`A_2=` area of small circle
`=pi(a/2)^2=(pia^2)/(4)`
`(x_1,y_1)=` coordinates of centre of mass of large circle `=(0, 0)`
`(x_2, y_2)=` coordinates of centre of mass of small circle `=(a/2, 0)`
Using `x_(COM)=(A_1x_1-A_2x_2)/(A_1-A_2)`
we get `x_(COM)=((pia^2)(0)-((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)`.