Question

The breaking load of the rope is half the weight of the climber in which of the following cases is the rope not likely to break?​

Answer 1

Given :

The breaking load of the rope is half the weight of the climber

To Find :

In which of the following cases is the rope not likely to break.

Solution :

(a) Climbing up fast

When the climber is climbing up the rope, the acceleration (a) of the climber is in upward direction whereas the acceleration due to gravity is acting downwards.

 Tension(T) - mass of the climber(m) × acceleration due to gravity(g) = ma

or,            T - mg = ma

∴                       T = ma + mg

(b) Climbing down fast

When the climber is climbing down the rope, the acceleration (a) of the climber is in downward direction and the acceleration due to gravity is also acting downwards.

                 mg - T   =   ma

∴                        T   = mg - ma

(c) Climbing up slowly

When the climber is climbing up slowly, we can assume that the acceleration is almost zero.

                T  = mg

(d) Climbing down slowly

When the climber is climbing down slowly, we can assume that the acceleration is almost zero.

                   T  = mg

∴ The tension in the rope is minimum in the second case i.e., when the climber is climbing down fast.

Hence the rope is least likely to break when the climber is climbing down fast.

∴ Correct option is (b) Climbing down fast.

Note : The question given is incomplete. Full question would be -

The breaking load of the rope is half the weight of the climber in which of the following cases is the rope not likely to break?​

(a) Climbing up fast

(b) Climbing down fast

(c) Climbing up slowly

(d) Climbing down slowly