Weigh It Underwater

Why it matters

No ruler fits a crown. But dip anything in water and it confesses its volume — and once you have mass AND volume, no fake metal can hide.

The idea in plain words

The book's two measuring methods. Tap them.

ρ = m ÷ V — measured two ways

A 50 cm³ density bottle weighs 40 g empty and 80 g full of oil. Density of the oil?

0.8 g/cm³ — lighter than water, so oil floats

• method 1: irregular solid — weigh it, then read its volume from the water it displaces in a measuring cylinder
• method 2: liquid (density bottle) — a small bottle that holds an exact volume: weigh empty, weigh full, divide the liquid's mass by the bottle's volume
• the yardstick: the reference — water: 1 g/cm³ = 1000 kg/m³ — everything is compared to it (that ratio is R.D.)
• mass of oil = 80 − 40 = 40 g
• ρ = 40 ÷ 50

Predict first

Two objects weigh the same in air. Underwater, the LESS dense one reads…

Less dense = bulkier for the same mass = displaces more water = gets a bigger upward discount on the scale.

• lighter — more volume, more upthrust — correct
• the same
• heavier

What you do

Weigh both pieces in air, dip them, and let the readings expose the fake.

Check yourself

Relative density compares a substance's density with…

R.D. = ρ(substance)/ρ(water): pure ratio, no units, same in every system.

R.D. of a metal is 8. Its density in kg/m³ is…

ρ = R.D. × 1000 kg/m³.

The crown reads lighter underwater than the equal-weight gold bar because the crown…

Same trick Archimedes used — the bath solved what the ruler couldn't.

• water's — correct
• air's
• iron's
• 8000 — correct
• 8
• 800
• has more volume (less dense) and so more upthrust — correct
• absorbs water
• is hollow of magic