Density – Mass per Volume സാന്ദ്രത
Why does a huge teak log float down the Periyar while a tiny iron nail sinks? Why does coconut oil sit on top of water? The answer is not “heavy or light” but density: how much mass is packed into each bit of volume. The chapter uses density everywhere. It decides the buoyant force, whether things float, and what a hydrometer and a lactometer measure. This page builds the idea from mass (page 1) and volume (page 2).
- Mass in g and kg (page 1); volume in cm³ and m³ (page 2).
- Dividing decimals and powers of ten.
1. Same size, different mass
Take a wooden ball and an iron ball of exactly the same size. They have the same volume, yet the iron ball is far heavier: in the same space, iron packs much more mass. To compare materials fairly, we ask: how much mass is there in one unit of volume? That is the density (സാന്ദ്രത):
The symbol ρ is the Greek letter “rho”. Density is a property of the material, not of the object. A small iron nail and a big iron rod have the same density, 7800 kg/m³, because if you cut a piece of 1 cm³ from either, it has the same mass.
Each dot is 10 g of mass, and the size of the square shows the volume. More dots in the same square means a denser material. Keep the mass fixed and make the volume bigger: the dots spread out and the density falls. Try 540 g in 200 cm³ (aluminium) and 100 g in 100 cm³ (water).
2. Units of density
Density is mass ÷ volume, so its unit is a mass unit ÷ a volume unit. In SI units it is kilogram per cubic metre, kg/m³; in the laboratory we often use gram per cubic centimetre, g/cm³. To convert, remember 1 g = 10⁻³ kg and 1 cm³ = 10⁻⁶ m³:
Water has a density of 1 g/cm³ = 1000 kg/m³: every cubic centimetre of water has a mass of 1 g, every litre 1 kg, and every cubic metre 1000 kg (a tonne).
Worked example 1 · What metal is it?
Q. A metal block has a mass of 540 g and a volume of 200 cm³. Find its density in g/cm³ and in kg/m³. Which metal could it be? (Use the table in section 3.)
ρ = m ÷ V = 540 ÷ 200. Multiply by 1000 to change g/cm³ into kg/m³, then look for that value in the table.
3. A table of densities
The liquids in the first part of this table are the ones in your textbook (Table 5.3, approximate values). Values marked “approx.” are not from the textbook; they are typical values, and real samples vary a little.
| Substance | Density (kg/m³) | g/cm³ | Compared with water |
|---|---|---|---|
| Kerosene (മണ്ണെണ്ണ) | 810 | 0.81 | less dense – floats on water |
| Coconut oil (വെളിച്ചെണ്ണ) | 920 | 0.92 | less dense – floats on water |
| Water | 1000 | 1.00 | — |
| Saturated salt solution (പൂരിത ഉപ്പുലായനി) | 1025 | 1.025 | denser |
| Glycerine (ഗ്ലിസറിൻ) | 1260 | 1.26 | denser |
| Mercury | 13 600 | 13.6 | much denser (textbook p. 104) |
| Iron | 7800 | 7.8 | denser – sinks |
| Copper | 8900 | 8.9 | denser – sinks |
| Brass (approx.) | ≈ 8500 | ≈ 8.5 | denser – sinks |
| Aluminium (approx.) | 2700 | 2.7 | denser – sinks |
| Ice (approx.) | 917 | 0.917 | less dense – floats |
| Wax (approx.) | ≈ 900 | ≈ 0.9 | less dense – floats |
| Teak wood (approx.) | ≈ 650 | ≈ 0.65 | less dense – floats |
| Air (approx., at room temperature) | ≈ 1.2 | ≈ 0.0012 | about 800 times less dense |
Density = mass ÷ volume, ρ = m/V. SI unit kg/m³; 1 g/cm³ = 1000 kg/m³. Water: 1000 kg/m³. Density belongs to the material: every piece of iron has the same density.
4. Same mass, different volume
Turn the formula around: V = m ÷ ρ. For the same mass, a denser material takes up a smaller volume. One kilogram of copper is a smaller block than one kilogram of iron, and one kilogram of teak is a big block. You will need exactly this idea on page 6, where the textbook compares an iron block and a copper block of equal weight (Table 5.4).
All five blocks balance each other on a common balance – same mass – but look at the sizes! The volumes are worked out as V = m ÷ ρ, and the cubes are drawn to the same scale.
Worked example 2 · Volume of 1 kg of iron
Q. Iron has a density of 7800 kg/m³. Find the volume of a 1 kg iron block, in m³ and in cm³.
V = m ÷ ρ = 1 ÷ 7800 m³. To change m³ into cm³, multiply by 10⁶.
5. Heavy is not the same as dense
A teak log on a timber lorry may weigh a tonne, while an iron nail weighs a few grams. The log is far heavier, but iron is far denser. Whether something floats in water depends on its density, not on its weight:
- Density of the object less than the liquid's → it floats (പൊങ്ങിക്കിടക്കുക), with part of it above the surface.
- Density of the object more than the liquid's → it sinks (മുങ്ങുക).
You will see why on pages 4–8. For now, test the rule. When an object floats, the fraction of it under the surface turns out to be ρobject ÷ ρliquid (page 8 explains this).
Ice in water: 917 ÷ 1000 ≈ 0.92, so about nine-tenths of an iceberg is hidden under the sea. Try iron in mercury – iron floats! Wax sinks in kerosene but floats in water. Densities are in kg/m³.
6. Liquids on liquids: oil on water
The same rule works for liquids that do not mix. Coconut oil (920 kg/m³) is less dense than water (1000 kg/m³), so oil poured into water rises and spreads as a layer on top. Kerosene does the same. When you wash a greasy vessel, the oil drops float to the top of the water.
Teak and bamboo logs were once floated down rivers like the Periyar and the Chaliyar to the timber markets: wood is less dense than water. A coconut falling into the backwaters floats away, and can grow on another beach. An oil spill from a boat spreads as a shiny film on top of Kochi harbour water. And at the milk society, the lactometer checks the density of milk to catch added water (page 9).
7. Check yourself
Next: Pressure in liquids ▶