Question

Obtain an expression for the centre of mass of a system consisting of two particle .

What is the physical significance of the centre of mass of a system.​

Answer 1

Expression for Centre of Mass :

• As per question, it is a binary system (i.e. 2 object system).

Now, coordinates of the objects be (x1,y1) and (x2,y2).

So, x coordinates of C-O-M will be :

$\bar{x} = \dfrac{ \sum( m_{i} x_{i})}{ \sum( m_{i})}$

$\implies\bar{x} = \dfrac{ m_{1} x_{1} +m_{2} x_{2} }{ m_{1} + m_{2}}$

And y coordinates will be:

$\bar{y} = \dfrac{ \sum( m_{i} y_{i})}{ \sum( m_{i})}$

$\implies\bar{y} = \dfrac{ m_{1} y_{1} +m_{2} y_{2} }{ m_{1} + m_{2}}$

So, the coordinates will be :

$\boxed{(\bar{x},\bar{y} )=(\dfrac{ m_{1} x_{1} +m_{2} x_{2} }{ m_{1} + m_{2}} , \dfrac{ m_{1} y_{1} +m_{2} y_{2} }{ m_{1} + m_{2}} )}$

Significance of centre of mass:

• It helps to understand the translational or rotational motion of a complex object which doesn't have a proper shape.