Two identical blocks are connected to the opposite ends of a compressed spring. The blocks initially slide together on a frictionless surface with velocity v to the right. The spring is then released by remote control. At some later instant, the left block is moving at v/2 to the left, and the other block is moving to the right. What is the speed of the center of mass of the system at that instant?

v

Explanation:

Given

Initially spring mass system is moving towards right with velocity

Now if the spring is released left block moves towards left with a velocity

As there is no external force applied on the system therefore the change in linear momentum is zero i.e. it is conserved

so center of mass continue to move towards the right with velocity v or we can say right block moves towards right with velocity and left block moves with velocity

whichever one it is, it's definitely not one that you included on the list you provided.

the answer is f1 and d2 because if you put equal force on those two points the beam would balance trust me on this