Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3 kg.

Explanation

The plate has uniform density and same thickness everywhere. So its CM will coincide with the centroid.
Divide the given plate two parts of area `A_(1)` and `A_(2)` as shown in the figure. We have
`A_(1)=2xx1m^(2)` with its centroid `C_(1)(1,1//2)` and
`A_(2)=1xx1m^(2)` with its centroid `C_(2)(1//2,3//2)`
the centroid of the whole plate can be defined as
`barx=(A_(1)x_(1)+A_(2)x_(2))/(A_(1)+A_(2))=(2xx1+1xx1/2)/(2+1)=5/6m`
`bary=(A_(1)y_(1)+A_(2)y_(2))/(A_(1)+A_(2))=(2xx1/2+1xx3/2)/(2+1)=5/6m`