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  • 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 ?

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 ?

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\\ \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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shubham.krishnan

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Dear candidate, as we know that there are three coordinates-x,y and z. An object lies in one plane, and one plane consists of only two coordinates. So if an object is lying in a X-Y plane, its z coordinate will automatically become zero,hence, the centre of mass will lie in the x-y plane only.

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ANJALI NAGAR

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