Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively.

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\frac{g}{2}, g

g, g

g, \frac{g}{2}

\frac{g}{2}, \frac{g}{2}

answer is B.

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Detailed Solution

Just before the string is cut, force on the spring pulling up = kx = 3mg
After string is cut, free body diagram of block A is as shown in figure(a)
$∴ 2 {ma}_{A} = 3 mg - 2 mg$ $\Rightarrow a_{A} = \frac{m g}{2 m} = \frac{g}{2}$
Free body diagram of block B as shown in figure (b)

$∴ m a_{B} = mg$
$\Rightarrow a_{B} = g$

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