Question

In order to raise a mass of 100 kg, a man of mass 60 fastens a rope it and passes the rope over a smooth pulley. he climbs the rope with acceleration 5 g/4 relative to the rope. the tension in the rope is (take g = 10 ms-2)

Answer 1

Before attempting to solve this question, you have to keep in mind that the acceleration of man that is given here is relative to the rope, which means that the acceleration of the 100kg mass has been included in it.
So, assuming the acceleration of 100kg mass as 'a', we take the acceleration of the man with respect to the ground frame (so that we can perform our calculations correctly) as
$( \frac{5g}{4} - a)$

Rest of the process is mentioned in the image.

Hope this helps.