In the figure shown a semicircular area is removed from a uniform square plate of side `l` and mass ‘m’ (before removing). The x-coordinate of centre of mass of remaining portion is (The origin is at the centre of square)

Options

A. `-(pi(pi-2)l)/(2(8-pi))`
B. `(pi(pi-2)l)/(2(8-pi))`
C. `-(pi(pi-2)l)/(8-pi)`
D. `-(l(pi-4/3))/(2(8-pi))`

Explanation

`x_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))`
`m_(1)`=mass of square plate
`=m`
`x_(1)`=c.m. of square plate =0
`m_(2)` =mass of removed part
`=-m/(l^(2))((pi(l^(2))/4)/2)=-(pi)/8 m`
`x_(2)`=c.m. of removed part
`=l/2-4/(3pi)(l/2)=l/2(1-4/(3pi))`
`:. x_(cm)=(-(pim)/8.l/2(1-4/(3pi)))/(m-(pi)/8m), x_(cm)=-(l(pi-4/3))/(2(8-pi))`