Question

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?

Answer 1

Explanation:

• Of course, if all the particles of a system lie in X-Y plane, it is necessary that the centre of mass be in X-Y plane.
• This is because, as all the particles lie in X-Y plane, the co-ordinates of Z for centre of mass are zero. We know that $z_{c m}=\left(m_{1} z_{1}+m_{2} z_{2}+\ldots+m_{n} z_{n}\right) / \sum m$. In this equation, the co-ordinates $z_1$, $z_2$ and $z_n$ are zero.  
• As a result, the whole system  $z_cm$ becomes zero and the centre of mass lies in the same X-Y plane.

Answer 2

Answer:

Yes , if all the particles of a system lies in X-Y plane then it's necessary that it's centre of mass lies in X-Y plane . As all the particles lies in the X-Y plane then Z co-ordinates are zero . Therefore, for the whole system Zcm = 0; i.e it's centre of mass lies in X-Y plane.

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