question_answer

One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in \[m{{s}^{-2}}\]) can a man of 60 kg climb on the rope?                             AIEEE  Solved  Paper-2002

A) 16   

B)                                             6

C) 4                                

D)           8

Correct Answer: C

Solution :

The free body diagram of the person can be drawn as                             Let the person moves up with an acceleration a, then                                          \[T-60g=60a\]                 \[\Rightarrow \,\,{{a}_{\max }}=\frac{{{T}_{\max }}=-60g}{60}\]                 \[=\frac{360-60g}{60}=\frac{360-600}{60}=-ve\]              which means it is not possible to climb up on the rope.                              Even in this problem it is not possible to remain at rest on rope.                                                              No option is right.                                     But if they will ask for the acceleration of climbing down, then \[60g-T=60a\]              \[\Rightarrow 60g-{{T}_{\max }}=60{{a}_{\min }}\]              \[\therefore \]     \[{{a}_{\min }}=\frac{60g-360}{60}=4\,m/{{s}^{2}}\]