Figure shows a ball of mas s m connected with two ideal springs of force constant k, kept in equilibrium on a smooth incline, suddenly right spring is cut. What is magnitude of instantaneous acceleration (in m/s²) of ball? 

Let initial extension in spring is x₀, then

$2k{x}_0\cos {45}^{\circ }=mg\sin {45}^{\circ }\Rightarrow 2k{x}_0=mg$

Let after cutting right spring, acc. of ball is A₁ along the inclined plane and a₂ perpendicular to a₁

$\begin{array}{l}\Rightarrow \frac{mg}{\sqrt{2}}-\frac{mg}{2}\frac{1}{\sqrt{2}}=m{a}_1\\ \Rightarrow a_1=\frac{g}{2\sqrt{2}}\end{array}$

Then

$\begin{array}{l}mg\sin {45}^{\circ }\Rightarrow k{x}_0\cos {45}^{\circ }=m{a}_1\\ k{x}_0\sin {45}^0=m{a}_2\Rightarrow a_2=\frac{g}{2\sqrt{2}}\end{array}$

$\text{ Net acceleration }a=\sqrt{a_1^2+a_2^2}=\frac{g}{2}=5\mathrm{m}/{\mathrm{s}}^2$