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Q.

The co-ordinates of centre of mass of particles of mass 10,20 and 30g are (1,1,1) cm. The position co-ordinates of mass 40g which when added to the system, the position of combined centre of mass be at (0,0,0) are____

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a

$(3 / 4, 3 / 4, 3 / 4)$

b

$(3 / 2, 3 / 2, 3 / 2)$

c

$(- 3 / 2, - 3 / 2, - 3 / 2)$

d

$(- 3 / 4, - 3 / 4, - 3 / 4)$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{10 x_{1} + 20 x_{2} + 30 x_{3}}{10 + 20 + 30} = 1 \Rightarrow 10 x_{1} + 20 x_{2} + 30 x_{3} = 60 \\ \frac{10 x_{1} + 20 x_{2} + 30 x_{3} + 40 x_{4}}{10 + 20 + 30 + 40} = 0 \Rightarrow 60 + 40 x_{4} = 0 \Rightarrow x_{4} = \frac{- 3}{2} \end{array}$

Simirarly

$y_{4} = \frac{- 3}{2}, z_{4} = \frac{- 3}{2}$

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