Final answer:
When one of the two ropes holding a box is cut, the tension in the remaining rope increases as it must support the entire weight of the box on its own.
Step-by-step explanation:
When a box of mass m is suspended by two ropes from a ceiling, and one of the ropes is cut, the tension in the remaining rope immediately doubles to support the entire weight of the box. The single rope now has to apply a force equal to the gravitational force on the mass m, which was previously shared by the two ropes.
Let's look at a similar scenario in an elevator for context: A mass of 2.0 kg is suspended by a rope. The tension when the elevator accelerates upward at 1.5 m/s2 would cause a tension of 22.6 N, while an acceleration downward at the same rate would produce tension of 19.6 N. These results indicate that the tension changes depending on the net forces acting on the mass.
In the initial situation with two ropes, each rope only needs to support half the weight of the object since the tensions are distributed equally. When one rope is cut, the entire weight of the object falls on the remaining rope, hence the tension in it increases to support the full weight of the object, which is equivalent to the gravitational force acting down on the object.