Find the position of centre of mass of the T-shaped plate from `O`, in Fig.

Explanation

Suppose `sigma` is mass per unit area of the plate.
`:.` Mass of horizontal portion `= 8 xx 2 sigma = 16 sigma`
Mass of vertical portion `= 6 xx 2 sigma = 12 sigma`
Centre of mass `O_(1)` of horizontal portion is such that `OO_(1) = 1m`.
Centre of mass `O_(2)` of vertical portion is such that `OO_(2) = 2 +3 = 5m`.
If `y` is distance of cm of T-shaped plate from `O`, then
`y = (16sigma xx 1+12 sigma xx 5)/(16 sigma + 12 sigma) = (76 sigma)/(28 sigma) = 2.71m`