Eureka!

Why it matters

King Hiero suspected his new crown wasn't pure gold. Archimedes had to prove it without melting it — and found the answer in his own overflowing bathtub. He ran home wet.

The idea in plain words

The principle, precisely. Tap the terms.

upthrust = weight of liquid displaced

A metal weighs 5.0 N in air, 4.5 N in water. Find its relative density.

R.D. = 10 — denser than water tenfold (silver territory)

• Archimedes' principle: the statement — a body in a fluid loses apparent weight equal to the weight of fluid it displaces
• the measurement: loss of weight — weight in air − weight in water = upthrust = ρ(liquid)·V·g
• the application: R.D. by Archimedes — R.D. = weight in air ÷ loss of weight in water — density testing without geometry
• loss = 0.5 N
• R.D. = 5.0 ÷ 0.5

Predict first

A crown and a gold bar weigh EXACTLY the same in air. Under water, the fake (less dense) crown will…

Less dense = more volume for the same mass = more water displaced = more upthrust = a bigger 'discount' on the scale. Water audits volume.

• read LIGHTER — bigger volume, more displaced water, more upthrust — correct
• read the same — same weight is same weight
• read heavier

What you do

Weigh both in air (identical), dip them, and let the water name the counterfeit.

Check yourself

Archimedes' principle applies to…

A hot-air balloon 'floats' on displaced cold air exactly as a ship floats on displaced sea.

A body displaces 200 cm³ of water when submerged. Its loss of weight is…

200 cm³ of water = 200 g = 0.2 kg → weight 2 N. Loss = displaced weight, always.

Two bodies of the SAME volume but different materials, both fully submerged, feel…

Same volume, same displaced water, same upthrust — the heavier one just SINKS despite it.

• liquids AND gases (balloons ride on it) — correct
• water only
• solids only
• 2 N (weight of 200 g of water) — correct
• 200 N
• 0.2 N
• the same upthrust — correct
• more upthrust on the heavier one
• more upthrust on the lighter one