Centres of mass

A uniform rod has its centre of mass at its mid-point. A non-uniform rod (e.g. a tree trunk)

would not necessarily have its centre of mass at its mid-point

Example: A non-uniform rod AB of mass 25 kg is of length 8 metres. Its centre of mass is

3 metres from A. The rod is pivoted about M, its mid point.

A mass of 20 kg is placed at P so that the system is in equilibrium. How far should this

mass be from the end A?

What is now the reaction at the pivot?

Solution: 

DRAW A DIAGRAM SHOWING ALL FORCES