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Centre of mass of two particles with masses 2kg and 1kg located at (1,0,1) and (2,2,0) has the co-ordinates of

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a

$(\frac{2}{3}, \frac{2}{3}, \frac{4}{3})$

b

$(\frac{2}{3}, \frac{4}{3}, \frac{2}{3})$

c

$(\frac{4}{3}, \frac{2}{3}, \frac{2}{3})$

d

$(\frac{1}{3}, \frac{2}{3}, \frac{2}{3})$

answer is A.

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Detailed Solution

$X_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}} = \frac{2 (1) + (1) (2)}{2 + 1} = \frac{4}{3} Y_{c m} = \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}} = \frac{2 (0) + 1 (2)}{2 + 1} = \frac{2}{3} Z_{c m} = \frac{m_{1} z_{1} + m_{2} z_{2}}{m_{1} + m_{2}} = \frac{2}{3}$

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