A) Climbs up with a uniform speed of 5 m/s
B) Climbs up with an acceleration of \[\text{6 m}/{{\text{s}}^{\text{2}}}\]
C) Climbs down with an acceleration of \[\text{4 m}/{{\text{s}}^{\text{2}}}\]
D) Climbs down with a uniform speed of \[\text{5 m}/\text{s}\]
Correct Answer: B
Solution :
The weight of the monkey \[=400\] Newton, while the breaking strength of the rope is \[600\] Newton. Thus the rope cannot break if the monkey suspends himself freely from the rope or when the monkey moves down the rope with some acceleration. It is so because when the monkey moves down the rope with acceleration, he is not able to exert full action of this weight on the rope. The greater the acceleration with which the monkey climbs down the rope, lesser is the tension in the rope, because he then derives only a little force from the force preventive his free fall. In fact, if the monkey comes down with an acceleration\[g\], he does not derive any force from the rope preventing his downward journey and so the tension in the rope in this situation is zero. So, option [c] and [d] cannot be correct. Thus the only possibility of the rope being broken arises when the monkey climbs up the rope due to the force of reaction he derives by pulling the rope downwards step by step. When the monkey rises up with uniform speed, the tension in the rope is just equal to the weight of the monkey. So option cannot be correct. The only option which talks about the monkey climbing upwards with acceleration is [b]. So the correct option is [b]. Mathematically, \[T-400=40\times 6\]or \[T=640\,\,N\] Since this tension is greater than the breaking strength of the ropes, the rope will break.
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