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  4. A block of mass m shown in figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light and smooth and strings light <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/85ce53f29ae41b6be135b74293e26f96-.png />

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Q. A block of mass $m$ shown in figure is in equilibrium. If it is displaced further by $x$ and released find its acceleration just after it is released. Take pulleys to be light and smooth and strings light
image

Laws of Motion

Solution:

image
Initially the block is at rest under action of force $2 T$ upward and $mg$ downwards. When the block is pulled downwards by $x$, the spring extends by $2x$ Hence tension $T$ increases by $2kx$ Thus he net unbalanced force on block of mass m is $4kx$
$\therefore $ Acceleration of the block
$=\frac{4 kx}{m}$