Two identical uniform rods of length `l` are joined to from `L` shaped frame, as shown is Fig. Locate the centre of mass of the frame.

Explanation

Let `m` be the mass of each rod. In Fig. `B` is taken as origin. `BC` is X-axis and `BA` is Y-axis. As the rods are uniform, their individual centre of mass must be lying at there respective centres, say `P` and `Q`. Thus the system is equivalent to two point masses `m` each, at `P (l//2,0)` and `Q(0,l//2)`
`:. x_(cm) = (mxxl//2 + m xx0)/(m+m) = l//4`
and `y_(cm) = (m xx 0 + m xx l//2)/(m + m) = l//4`
Hence centre of mass of the system is at `O(l//4 , l//4)`.