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, then2kx0cos⁡45∘=mgsin⁡45∘⇒2kx0=mgLet after cutting right spring, acc. of ball is A1 along the inclined plane and a2 perpendicular to a1⇒ mg2−mg212=ma1⇒ a1=g22Thenmgsin⁡45∘⇒kx0cos⁡45∘=ma1kx0sin⁡450=ma2⇒a2=g22 Net acceleration a=a12+a22=g2=5m/s2