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Four particles A,B,C and D with masses $m_{A} = m, m_{B} = 2 m, m_{C} = 3 m$ and $m_{D} = 4 m$ are at the corners of a square. They have accelerations as shown. The acceleration of centre of mass of the particles is

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$\frac{a}{5} (\hat{i} + \hat{j})$

$\frac{a}{5} \hat{j}$

$\frac{a}{5} (\hat{i} - \hat{j})$

$\frac{a}{5} \hat{i}$

answer is A.

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Detailed Solution

$\bar{a_{C M}} = \frac{m_{1} \bar{a_{1}} + m_{2} \bar{a_{2}} + m_{3} \bar{a_{3}} + m_{4} \bar{a_{4}}}{m_{1} + m_{2} + m_{3} + m_{4}}$

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