Newtons Laws Of Motion

Let the mass of the fireman be , and let the tension in the rope be . As the fireman slides down with acceleration , we apply Newton’s second law: Given that the maximum breaking strength of the rope is of the fireman's weight: Substituting for : So, the minimum acceleration the fireman must slide down with to prevent the rope from breaking is .

Action and reaction are equal in magnitude and opposite in direction according to Newton's third law of motion. However, they act on different bodies. Because of this, they cannot cancel each other out. They do not balance each other since they act on separate objects.
Thus, the correct answer is (B).