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Two bodies of masses 10kg and 20kg are located in x-y plane at $(0, 2)$ and $(2, 0)$ . The position of their centre of mass is

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

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

$(\frac{1}{3}, \frac{4}{3})$

$(2, 1)$

answer is A.

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Detailed Solution

$\begin{aligned} x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}} \\ y_{c m} = \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}} \end{aligned}$

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