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

Explanation

As ice is floating, `W=Th`, ice `Vrhog=V_(in)sigma_(W)`. Now if `A` is the cross section of the block ,`L` its thickness and out of `L, h` is inside water, `V=AL` and `V_(in)=Ah`

`Alrho_("ice")=hArho_("water")`
`h=rho_("ice")/rho_("water")LK=0.9xx5=4.5m`
i.e., `4.5 m` of ice will be submerged in water. So the level of water in the hole will be `5-4.5=0.5 m` below the top of ice and hence the length of rope required to scoop up water is `0.5 m`.