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Position vector of a particle of mass 2kg is $2 \hat{i} + \hat{j}$ . Position vector of another particle of mass ‘m’ is 5i – xj. If position vector of the center of mass of both particles is 3i-2j, the value of ‘x’ is

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answer is B.

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Detailed Solution

$(m_{1} + m_{2}) {\vec{r}}_{C M} = m_{1} {\vec{r}}_{1} + m_{2} {\vec{r}}_{2}$

$(2 + m) (3 i - 2 j) = 2 (2 i + j) + m (5 i - x j)$

$(6 + 3 m) i - (4 + 2 m) j = (4 + 5 m) i + (2 - m x) j$

$\begin{array}{l} 6 + 3 m = 4 + 5 m \Rightarrow m = 1 \\ 4 + 2 m = m x - 2 \Rightarrow x = 8 \end{array}$

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