CBSE-XI-Physics
09: Centre of Mass, Linear Momentum, Collision
- #3If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?Ans : 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 }_{i=1}^{i=n}\left(∆{m}_{i}\right){x}_{i}``
`` Y=\frac{1}{M}{\sum }_{i=1}^{i=n}\left(∆{m}_{i}\right){y}_{i}``
`` Z=\frac{1}{M}{\sum }_{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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