Two object of mass 5.0kg and 2.0kg are hung 0.6m from the floor on the ends of a strong string of length 6.0 m

Question

over a smooth pulley .Both object start from rest . find the maximum height by the 2.0kg object

Answer 1

Assuming the 4.8 m is like for a table or something...
net force is greater on 5kg side, so it will keep going until it is 1.2 meters off the ground (2 times original)

Answer 2

1.2 meters.

This mechanism, BTW, is called an 'Atwood machine'.

HTH

Doug