Question

Is it necessary that a mass should be present at the centre of mass of any system?

Answer 1

no, It's not necessary that a mass should be present at the centre of mass of any system.

for better understanding let's take an example !
take four tiny particles , each of mass m and these are located in vertices of square of edge length l as shown in figure.

centre of mass , (x , y)

x = $\frac{m_1x_1+m_2x_2+m_3x_3+m_4x_4}{m_1+m_2+m_3+m_4}$
= (m × -l/2 + m × l/2 + m × l/2 + m × -l/2 )/(4m)
= 0

similarly, y = $\frac{m_1y_1+m_2y_2+m_3y_3+m_4y_4}{m_1+m_2+m_3+m_4}$
= (m × l/2 + m × l/2 + m × -l/2 + m × -l/2)/(4m)
= 0

hence, centre of mass is located at (0,0) .

here it is clear that each tiny particle doesn't present in origin but centre of mass of whole system of particles present in origin.

Answer 2

Hii dear,

◆ Answer-
No. It's not necessary that a mass should be present at the centre of mass of any system.

◆ Explanation-
The center of mass may be located outside the physical body where there's no mass present, as is the case for -
- hollow sphere,
- hollow cylinder,
- hollow cube,
- open vessel,
- ring,
- horseshoe, etc.

Hope that was useful...