Question

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

• A. $\frac{4kx}{5m}$
• B. $\frac{2kx}{5m}$
• C. $\frac{4kx}{m}$
• D. none of these

Answer 1

Answer: (C)

Initially the block is at rest under action of force $2T$ 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
$=\frac{4kx}{m}$