Show that the centre of gravity of three equal weights suspended from three vertices of a triangle coincide with the centre of mass of the triangle.

Show that the centre of gravity of three equal weights suspended from

1.	Show that the centre of gravity of three equal weights suspended from three vertices of a triangle coincide with the centre of mass of the triangle.
Answer» Solution :Let a median of the triangle ABC be AD Fig. Identical weights W are hung from each of the VERTICES A,B and C. RESULTANT of the weights suspended from B and C = 2W and it acts from the point D. Resultant of the forces 2W at D and W at A is 3W. SUPPOSE this resultant acts at G. Hence `WxxAG=2WxxDG` or, AG=2DG THUS, G is the point of intersection of the medians of the triangle, which is the centre of mass.