# Circular motion of two connected balls

I came across the following problem: Two balls A and B of mass 1kg and 4kg respectively are connected by an ideal string and placed on a smooth horizontal surface. A and B are given velocity perpendicular to string. Motion of ball is in horizontal plane. Then find tension in string. I have found the tension in the string but I was thinking about the type of motion that the balls will undergo and apparently came up with some contradictions. My expectation: Since external force on system(in horizontal plane) is zero The COM should be moving in a straight line. So at a later time t the com would have moved a distance $$d=V(COM)t$$ along the line l as shown( $$V(COM)$$ being the velocity of COM which is supposed to be constant)

Now since COM should be on the line joining A and B, The string should so pass through COM(if taut). But in that case $$V(A)$$ and $$V(B)$$ should be perpendicular to the string as shown which clearly implies that $$V(COM)$$ won't be along the drawn line So summing up my question

2. What type of motion will the system execute?( Would be great if the equation is stated along with the derivation)