If the system is released, then the acceleration of the centre of mass of the system is

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$g$

$2 g$

$\frac{g}{2}$

$\frac{g}{4}$

answer is A.

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Detailed Solution

$a = (\frac{3 m - m}{3 m + m}) g = \frac{g}{2}$
Acceleration of centre of mass
$= \frac{3 m \times \frac{g}{2} - \frac{m g}{2}}{3 m + m} = \frac{g}{4}$

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