Question

What is the meaning of density in terms of Archimedes principle? [3 Marks]

Answer 1

If you drop a lump of clay in water, it will sink. But if you mold the same lump of clay into the shape of a boat, it will float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same is true of steel ships. [1 Mark]

The average density of an object is what ultimately determines whether it floats. If an object’s average density is less than that of the surrounding fluid, it will float. The reason is that the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink. [1 Mark]

The extent to which a floating object is submerged depends on how the object’s density compares to the density of the fluid .
fraction submerged
=$V_{sub}/V_{obj}$
=$V_{fl}/V_{obj}$
= $(M_{fl}\times D_{fl})/(M_{obj}\times D_{obj}$)
= $D_{fl}/D_{obj}$

We can use this relationship to measure densities. [1 Mark]