center of mass

 A point which entire mass of body or system of bodies is supposed to be concerned is known as the center of mass

key point

The center of masss of  s system of particles is the point that moves as though (1) all of the system's mass w

center of Mass of a two particle System

 figure shows two particles of masses m1 and m2 seperated by distance d. We have arbitrarily chosen the origin of an x axis to coincide with the particle of mass m1. we define the position of the center of mass (com) of this two particle system to be

suppose m2=0. Then there is only one particle, of mass m1 and center of mass must lie at the position of that particle . in this case equation reduces to xcom =0. If m1 =0, there is again only one particle(of mass m2), and we have , xcom =d. if m1 = m2, the center of mass is halfway between the two particles,and eq6.10 reduces to x com =1/2d . Finally eq(6.1)tells us that if that neither m1 nor m2 is zero , x com can have only values that lie between 0 and d, that is center of mass must lie somewhwere between the two particles.

figure b shows more generalized situation , in which the co ordinates system has beeen shifted leftward. the position of the center of mass is now defined asere concentrated  there and (2) all external forces were applied there.