Question

Consider a large cube of ice floating in seawater. The specific gravities of ice and seawater are 0.92 and 1.025 respectively. If a 10 cm high portion of the cube extends above the surface of the water, determine the height of the ice block below the surface.

Answer 1

Let the volume of the block be v. Its weight will be 0.92*v*g*di where di is the density of ice and g is the accn due to gravity.

The displaced volume of seawater (vd) must be such that its weight is 0.92*v*g*di, so we can write-
vd*1.025*g = 0.92*v*g*d
vd/v = 0.898

Since the block is a cube, volumes are proportional to height, so we can write hs/h = 0.898 where hs is the submerged height.

hs/(hs + 10 ) = 0.898

hs = 88.0 cm