Complete Question 
 The diagram for this question is shown on the first uploaded image 
Answer:
 The minimum velocity of A is  
Explanation:
From the question we are told that 
     The length of the string is  
      The initial speed of block A is 
      The final speed of block A is  
       The initial speed of block B is 
       The mass of block A  is   gh
  gh
       The mass of block B is  
 According to the principle of conservation of momentum 
        
Since block B at initial is at rest 
        
        
 
           
   making  the subject of the formula
 the subject of the formula 
              
Substituting values 
                 
   
This  is the velocity at bottom of the vertical circle just at the collision with mass A
 is the velocity at bottom of the vertical circle just at the collision with mass A
Assuming that block B is swing through the vertical circle(shown on the second uploaded image ) with an angular velocity  of  at  the top of the vertical circle
 at  the top of the vertical circle  
  The angular centripetal acceleration  would be mathematically represented 
                    
Note that  this acceleration would be toward the center of the circle 
       Now the forces acting at the top of the circle can be represented mathematically as 
          
     Where T is the tension on the string 
   According to the law of energy conservation 
 The energy at  bottom of the vertical circle   =  The energy at the top of 
                                                                                 the vertical circle 
    This can be mathematically represented as
                  
From above   
                 
Substitute this into above equation 
               
   
              
           
The  value of velocity of block A needed to cause B be to swing through a complete vertical circle is would be minimum when tension on the string due to the weight of B is  zero 
         This is mathematically represented as 
                       
making   the subject
 the subject 
             
substituting values 
           
               