Question

A block of mass $2kg$ is hanging with two identical massless springs as shown in figure. The acceleration of the block at the moment the right spring breaks is $(g=10m/s^2)$

• A. $10m/s^2$
• B. $5m/s^2$
• C. $25m/s^2$
• D. $4m/s^2$

Answer 1

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

Before cutting, FBD of the block is

$2kx\cos {60}^{\circ }=mg$
$\Rightarrow kx=mg$

After cutting, FBD is


Net vertical force $F_y=mg-kx\cos {60}^{\circ }=kx-kx\cos {60}^{\circ }$
($\because mg=kx$)
$F_x=kx-\frac{kx}{2}=\frac{kx}{2}$
Net horizontal force $=kx\sin {60}^{\circ }=kx\times \frac{\sqrt{3}}{2}$
Therefore net force on block after thread is cut $=\sqrt{F_x^2+F_y^2}=kx$

Then, $kx=ma$
$⟹mg=ma$
$⟹a=g=10m/s^2$