Why a Heavy Iron Ship Floats but a Small Nail Sinks

Because floating depends on density, not weight. A ship is mostly hollow, so the whole ship — steel plus the air inside — is less dense than water, while a solid nail is not.

So the question is never "how heavy is it?" but "how heavy is it for its size?" This page covers everything in the ICSE Class 7 Physics chapter's second half: density and its units, measuring density in the laboratory, relative density, and the rule for floating and sinking.

Measure the mass on a beam balance and the volume by the method that suits the shape, then divide.

Regular solid. A cube of side $2cm$ has volume $2^3=8c{m}^3$. If its mass is $21.6g$, then

$$\rho =\frac{21.6}{8}=2.7g/c{m}^3$$

Irregular solid. Find the volume by water displacement. Suppose a metal piece has mass $78g$, and the water level rises from $40mL$ to $50mL$, giving a volume of $10c{m}^3$:

$$\rho =\frac{78}{10}=7.8g/c{m}^3$$

which identifies the metal as iron.

Liquid. Weigh an empty measuring cylinder, add a known volume of the liquid, and weigh again. If the empty cylinder is $45g$, the cylinder with $50c{m}^3$ of oil is $88g$, then the oil's mass is $88-45=43g$ and

$$\rho =\frac{43}{50}=0.86g/c{m}^3$$

The step students forget is subtracting the container's mass. Weighing the filled cylinder alone measures glass plus liquid, and using that figure would make every liquid look far denser than it is.

Relative density, also called specific gravity, is the density of a substance compared with the density of water at $4°C$:

$$\text{R.D.}=\frac{\text{density of the substance}}{\text{density of water at }4°C}$$

It has no unit because it is a ratio of two densities — the units cancel, leaving a bare number.

Worked example. Iron has density $7.8g/c{m}^3$ and water $1g/c{m}^3$, so

$$\text{R.D. of iron}=\frac{7.8}{1}=7.8$$

meaning iron is 7.8 times as heavy as an equal volume of water.

Water at $4°C$ is chosen as the reference because water is at its densest then, giving a fixed standard that does not drift with room temperature.

The numerical convenience is worth noticing: in CGS units, water's density is exactly 1, so the relative density of a substance is the same number as its density in $g/c{m}^3$. A substance of density $2.7g/c{m}^3$ has relative density 2.7.

But they are not the same quantity. Density carries a unit and relative density does not, so writing "R.D. $=7.8g/c{m}^3$" is marked wrong.

Compare the body's density with the liquid's. If the body is less dense, it floats; if more dense, it sinks; if equal, it stays wherever it is placed, fully submerged.

Against water at $1g/c{m}^3$:

- Cork, about $0.24g/c{m}^3$ — floats, and rides high because it is so much lighter.
- Ice, $0.92g/c{m}^3$ — floats, with about 92 percent of it below the surface.
- Iron nail, $7.8g/c{m}^3$ — sinks.
- Wax, about $0.9g/c{m}^3$ — floats in water but sinks in a lighter liquid such as spirit.

That last case is the point often missed: floating is not a fixed property of an object. It depends on the pair of densities, so the same wax behaves differently in different liquids.

Ice floating matters beyond the classroom. Because solid water is less dense than liquid water, ice forms a floating layer on a pond rather than sinking, and the water beneath stays liquid enough for fish to survive a hard winter.

And the ship from the opening now resolves cleanly. Its hull encloses a large volume of air, so the average density of ship plus air is below $1g/c{m}^3$. Let water into the hull and that average rises past water's density, which is exactly what sinking means.