Relation between Tension and net force

[Mr.Y]

I am having a lot of difficulty understanding this concept.

Suppose you have two objects A,B of mass A',B' connected by a massless rope. Let K Newtons be the force applied on object A .What is now the tension along the rope ?


-My reasoning:

K Newtons is the force applied to the combination of masses A'+B' ,now to find the tension along the rope we have to find the forces acting on the rope.

Applying a force to object A we have by Newton's third that F (AR)=-F(RA) where AR denotes the force of A on the rope and viceversa.

Similarly, F(BR)=-F(RB) .

So the forces acting on the ropes are -F(RA)-F(RB)=F(BR)+F(AR) ,since the rope is massless I have that F(BR)=F(AR) so I just need to find one of these two forces to find the tension.

Now this is the part that's really confusing to me :we could have also found the tension by setting up the equation K-T=F(AR) ,where T denotes the tension. So solving the last equation we find the tension along the rope,but why ?
Can you give me both an intuitive argument and also show me where this follows from just mathematical formalism ? (I hope I am not asking too much )

 

[Nidum]

The question is poorly defined but let us assume that masses are sitting on a level plane and that there are no friction forces acting .

When the force is applied to mass A what do you expect to happen physically ?

 

[Mr.Y]

I would expect the rope to exert the same force to object A in the opposite direction.
(Yes sorry I have forgot to define if there's friction and the direction of the forces,bear with me !)