Two identical uniform rods AB and CD, each of length L are jointed to form an inverted T-shaped frame as shown in figure. Locate the centre of mass of the frame. The centre of mass of a uniform rod is at the middle point of the rod.

Explanation

Let the mass of each rod be m. Take the centre C of the rod AB as the origin and CD as the Y-axis. The rod AB has mass m and its centre of mass is at C. For the calculation of the centre of mass of the combined system, AB may be replaced by a point particle of mass m placed at the point C.
Similarly the rod CD may be replaced by a point particle of mass m placed at the centre E of the rod CD. Thus, the frame is equivalent to a system of two particles of equal masses m each, placed at C and E. The centre of mass of this pair of particle will be at the middle point F of CE. The centre of mass of the frame is, therefore, on the rod CD at a distance L/4 from C.