A large block of ice $5 m$ thick has a vertical hole drilled through it and is floating in the middle of a lake. The minimum length of the rope required to scoop up bucket full of water through the hole is (the relative density of ice $=0.9$) 

Let $h$ be the height of the block $x=0.9h$

and  $A$  its area of cross-section.

 Weight of ice block $=Ahg\times 0.9$

 If $x$ is the height of the block immersed in water,

 then the weight of water displaced $=A\times g$.

 Equating the two we get  $x=0.9h$

 Height above the surface of water 

= h$\mathbf{-}$0.9 h = 0.1 h = 0.1 x 5 m = 0.5 m..