The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The buoyant force upward on the iceberg is gonna equal the weight of the iceberg because it's floating. So the buoyant force will be the density of sea water multiplied by the volume of sea water displaced so that's by... this is the volume of the iceberg which is within the sea water and then times g. And this over here on the right hand side is the density of the iceberg times the volume of the entire iceberg— the part above and the part below included in this V i— and the g's cancel and we get V displaced divided by total volume of the iceberg equals density of the iceberg divided by density of seawater when you rearrange this. So this is the fraction of the iceberg which is submerged because this volume displaced equals the volume of the iceberg within the seawater. So specific gravity is defined as the density of whatever divided by the density of water so for the iceberg, it's gonna be density of the iceberg divided by density of water and we can solve for the density of the iceberg which we are gonna put in here— specific gravity times the density of water— and same idea for the seawater— specific gravity of seawater times the density of water— and substitute both of those into here and we see that the densities of the water's just cancel so the ratio of the volume displaced to the total volume of the iceberg is the ratio of their specific gravities. So that's 0.917—specific gravity for the ice— divided by 1.025—specific gravity for the seawater— that gives 0.8946 and the percent of the iceberg above the water is gonna be the total 1 minus this 89 percent submerged which gives about 10.5 percent above the water.