How are two unequal applied forces at the end of a massless string result in a constant tension throughout?

Question

Even when we apply two different forces $(F_1 > F_2)$ at the ends of an ideal rope, the tension produced in the rope is constant throughout the length of the string rather than being a function of its length. I can't understand this concept, I mean taking any arbitrary element in the rope the element would be experiencing two unequal forces at its two ends so how does that make a common tension? Why is tension not equal to the net resultant force $(F_1 - F_2)$? Is tension different than a force?

Answer 1

If the rope is "light", then it is not possible to apply unequal forces to the ends. Unequal forces imply acceleration. And if the mass is approximately zero, the acceleration is huge. The forces on each end and the tension within are all equal.

If you consider the rope to have mass, then unequal forces are possible, but only if the rope accelerates. The tension throughout the rope is not equal because the mass that any section of the rope is pulling on to accelerate differs from one side to the other.