# If All the Particle of a System Lie in a Cube, is It Necessary that the Centre of Mass Be in the Cube? - Physics

Short Note

If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?

#### Solution

Yes. As a cube is a 3-dimensional body, all the particles of a system lying in a cube lie in the x,y and z plane.

Let the ith element of mass ∆mi is located at the point (xi,yi,zi).
The co-ordinates of the centre of mass are given as:

$X = \frac{1}{M} \sum\nolimits_{i = 1}^{i = n} \left( ∆ m_i \right) x_i$
$Y = \frac{1}{M} \sum\nolimits_{i = 1}^{i = n} \left( ∆ m_i \right) y_i$
$Z = \frac{1}{M} \sum\nolimits_{i = 1}^{i = n} \left( ∆ m_i \right) z_i$

X, Y and Z lie inside the cube because it is a weighted mean.

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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
Short Answers | Q 3 | Page 156