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In the figure shown, pulley and spring are ideal and strings are light and inextensible. Initially all the bodies are at rest when string connecting A and B is cut. Find initial acceleration (in m/ s²) of pulley.

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answer is 5.

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Spring force does not change instantly. Just after cutting the string, spring force will be 4mg . Since, pulley is massless, tension in the string will be still 2mg .
$a_{A} = \frac{2 mg - mg}{m} = g ↑ and a_{C} = 0$
So, $a_{pulley} = \frac{(g + 0)}{2} = 5 m / s^{2}$

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In the figure shown, pulley and spring are ideal and strings are light and inextensible. Initially all the bodies are at rest when string connecting A and B is cut. Find initial acceleration (in m/ s2) of pulley.