All springs, string and pulley shown in figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of block $m$ is $\frac{x m g}{5 k}$ . Then x is:

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Solution

The correct option is D 2
Let the upper spring elongates by $x$
then the lower spring streches by $2 x$ and so the block lowers by $2 x$
applying conservation of energy
Loss in Potential energy of block= energy stored in springs
$m g (2 x) = \frac{1}{2} K x^{2} + \frac{1}{2} K (2 x)^{2}$
solving we get
$x = \frac{4 m g}{5 k}$

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All springs, string and pulley shown in figure are light. Initially when both the springs were in their natural state, the system was released from rest. The maximum displacement of block m is xmg5k. Then x is:

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