Question

Mass $4kg$ as shown in the figure is in equilibrium. If it is displaced further by $10cm$ and released, find it's acceleration just after the release. Consider pulleys to be light & smooth and strings very light.

• A. $10m/s^2$
• B. $20m/s^2$
• C. $5m/s^2$
• D. None of these

Answer 1

The correct option is A $10m/s^2$

Initially the system is in equilibrium. Here weight of the body balances the initial strecth of the spring.
Also,
$T=k{x}_s$
Now, Stretching by a distance x, will cause the block to oscillate.
Further if the block is stretched by x, there is corresponding twice the elongation of spring.
$x_s=2x$
So net disturbance for block will be $=2T=2\left(2kx\right)$
This disturbance will make the block to accelerate. Therefore,
$a=4kx/m=10\frac{m}{s^2}$
Answer is A.