Answer:
Choice d. Approximately
of the volume of this iceberg would be submerged.
Explanation:
Let
denote the total volume of this iceberg. Let
denote the volume of the portion that is under the liquid.
The mass of that iceberg would be
. Let
denote the gravitational field strength (
near the surface of the earth.) The weight of that iceberg would be:
.
If the iceberg is going to be lifted out of the sea, it would take water with volume
to fill the space that the iceberg has previously taken. The mass of that much sea water would be
.
Archimedes' Principle suggests that the weight of that much water will be exactly equal to the buoyancy on the iceberg. By Archimedes' Principle:
.
The buoyancy on the iceberg should balance the weight of this iceberg. In other words:
.
Rearrange this equation to find the ratio between
and
:
.
In other words,
of the volume of this iceberg would have been submerged for buoyancy to balance the weight of this iceberg.