Question

Figure shows a rod of mass 10 kg of length 100cm with some masses tied to it at different position. Find the point on the rod at which if the rod is picked over a knife edge, it will be in equilibrium about that knife edge.

Answer 1

Centre of mass of the system shown in figure, will be the point, at which if we place a knife edge, system will remain in equilibrium.
To locate the centre of mass of the system, we consider origin at the left end of the rod. With respect to this origin the position of centre of mass of the system is
`x_(c)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4)+m_(rod)x_(rod))/(m_(1)+m_(2)+m_(3)+m_(4)+m_(rod))`
`x_(c)=(25xx0+8.5xx30+10xx50+5xx80+5xx90)/(53.5)=30cm`