Question

A large block Of ice 4m thick has a vertical hole drilled through it and it's floating in the middle of water in a lake . Three minimum length of rope required to scoop up a bucket full of water through the hole is

Answer 1

Minimum length of rope  $x=40\ cm$

The remaining part of the question is: The minimum length of rope required to scoop up a bucket full of the through the hole is (density of ice =0.9CGS unit, density of water =1CGS unit).

Explanation:

According to the given density and thickness of the ice cube it will float on the surface of water with some height submerged into the water.

• Let x be the depth below which the part of ice is submerged and we need to the minimum length of rope to be x.

Now the weight of the ice will be balanced by the upthrust of the water.

$V.\rho_i.g=V_{in}.\rho_w.g$

$(A\times 4)\ \rho_i=A\times (4-x) \rho_w$

$\frac{\rho_i}{\rho_w} =\frac{4-x}{4}$

$0.1=\frac{4-x}{4}$

$x=0.4\ m$

$x=40\ cm$