Find the centre of mass of a uniform `L` shaped lamina (a thin flat plate) with dimension as shown in Fig. The mass of the lamina is `3kg`.

Explanation

The L-shaped lamina is divided into three squares of side 1 m each. The lamina is uniform, so the mass of each square is 1 kg. By symmetry, centres of mass of the three squares lie at their geometric centres `O_(1),O_(2)` and `O_(3)`. The points along with their coordinates can be written as:
`O_(1)((1)/(2),(1)/(2)),O_(2)((3)/(2),(1)/(2))andO_(3)((1)/(2),(3)/(2))`
So the centre of mass of lamina is:
`X_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`=(1xx(1)/(2)+xx(3)/(2)+1xx(1)/(2))/(1+1+1)=(5)/(6)m`
`Y_(cm)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))`
`=(1xx(1)/(2)+1xx(1)/(2)xx1xx(3)/(2))=(5)/(6)m` Centre of mass lie at the line of symmetry OD.