Final answer:
The mass of the rope does not change when you increase the force applied while pulling on it. The tension, acceleration, and force applied will change, but the mass, being an intrinsic property, will remain constant.
Step-by-step explanation:
When you increase the force that you apply while pulling on a rope, the mass of the rope is not affected. The tension in the rope (a), the acceleration of the rope (b), and the force applied to the rope (c) are all factors that will change with an increase in the force applied. However, the mass of the rope (d) remains constant as it is an intrinsic property of the rope that does not change due to the force applied during the pulling.
The principle guiding this outcome is derived from Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). Thus, as you increase the force (tension), you also increase the acceleration, assuming mass remains unchanged. The mass of an object is an inherent characteristic that does not change with the force applied in this context.