What fraction of an iceberg is submerged? (ρice = 917 kg/m3, ,ρsea = 1030 kg/m3.)

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.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft