obtain an expression for position vector of centre of mass of a two particle system - Physics - System Of Particles And Rotational Motion

Question

obtain an expression for position vector of centre of mass of a
two particle system

Shikha Bhadoria · Accepted Answer

Centre of Mass of System of two Particles

Let us consider a system of two particles having mass m1 and m2 Let the distances of two particles be x1 and x2 respectively from some origin O The centre of mass of the system is that point C, which is at a distance X from O, where X is given by,

So, the position vector is: $\vec{r} = X \hat{i}$ If, the masses are placed in the plane such that m1 is at (x1,y1) and m2 is at (x2,y2) This means the position vector of m1 and m2 is: $\vec{r_{1}} = x_{1} \hat{i} + y_{1} \hat{j} \vec{r_{2}} = x_{2} \hat{i} + y_{2} \hat{j}$ Then, by going on same lines as before we obtain X (as (i)) and Y $\vec{r_{c m}} = X \hat{i} + Y \hat{j}$