The system shown in the figure is released from rest. The spring gets elongated
(Neglect the friction and masses of pulley, string, and spring.)

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$If M > m$

$If M > 2 m$

$If M > m / 2$

$For any value of M$

answer is D.

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Detailed Solution

Let spring does not get elongated, then net pulling force on the system is $M g + m g - m g$ or simply Mg. Total mass being pulled is $M + 2 m$ . Hence, acceleration of the system is $a = \frac{M g}{M + 2 m}$

Now since a < g, there should be an upward force on M so that its acceleration becomes less than g. It means there is some tension developed in the string. Hence, for any value of M spring will be elongated.

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