We can see that the block A and block C are connected to block B by inextensible strings passing over light frictionless pulleys.
All the three blocks have mass m
Acceleration on each block of mass m is equal to F/3m
Thus, external net force acting on cart is zero. Thus, net acceleration acting on cart is zero.
Let's solve 13b)
The question says, find the magnitude of tension in the string connecting block B and block C.
By using Newton's second law of motion on block C we can find the tension in the string connecting block B and C
We know, the acceleration on block C is F/3m
Tension will be given as,
T = ma = m x (F/3m) = F/3
Thus, magnitude of tension in the string connecting block B and C is F/3