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

Solution: Let the mass of each rod be m. Tke the centre C of the rod AB as the origin andCB as the Y-axis. The rod AB hs 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 piont C. Similarly the rod CB may be replaced by a point particle of mas m placed at teh centre E of the rod CD. Thus the framed is equivalent to a system of two particles of equal masses m each, placed at C and E. The centre of mass masses m each, placed at C and E. Teh centre of mass of this pair of particles 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.