# If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane ?

$\\ \text{Yes, if all the particles of a system lie in the X-Y} plane, then it's necessary that its centre of mass lies in the X-Y plane.\\ As we know, z_{c m}=\frac{m_{1} z_{1}+m_{2} z_{2}+\ldots m_{n} z_{n}}{\sum m} \\ As all the particles lie in the X-Y plane, their z -coordinates are zero. \\ Therefore, for the whole system, z_{\mathrm{cm}}=0 ; i.e., its centre of mass lies in the X-Y plane.$

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