In the figure shown C is a fixed wedge on horizontal surface. Blocks A and B are of masses m and 2 m respectively are kept as shown in figure. They can slide along the inclined plane smoothly. The pulley and string are massless. Take θ=30o and g = 10 m/s2. The inclined planes are very Long. A and B are released from rest. 2 seconds after the release, B is caught for a moment and released again. Find out the speed of A just before the instant when the string becomes tight again.

Initially acceleration of B and A is same along the string which is given by a=2mgsin⁡30∘−mgsin⁡30∘3m=g6After 2 seconds, speed of both A and B isvB=vA=g6×2=103m/sNow, when B is caught for a moment and released again, speed of B becomes zero, while A is still having a speed 103m/s up the inclined due to which string will become slack. But A will decelerate and B will accelerate. Because of this the string will become tight again after A and B travel the same distance. Let this time interval be t103×t−12gsin⁡30∘×t2=12gsin⁡30∘×t2⇒ 103=g2t as t≠0t=23secAt this time speed of A is given byv=103−g2×t=103−102×23=0