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Relative Density (Specific Gravity)

Simple Explanation

Relative density (also called specific gravity) compares a substance's density directly to water's density: RD = ρ(substance)/ρ(water). Since it is a ratio of two densities, it has no units β€” a relative density above 1 means the substance sinks in water; below 1 means it floats.

Why Do We Need It?

Relative density is a convenient, unit-free number that instantly tells you whether something floats or sinks in water, and is widely used in industry to test liquids like battery acid, milk, and fuel for concentration or purity.

Formula

Relative Density (Specific Gravity)

RD = ρ(substance) / ρ(water)

Relative density compares a substance's density directly against water's β€” a relative density greater than 1 means the substance is denser than water (and sinks in it); less than 1 means it is less dense (and floats).

RD
β€” relative density (specific gravity) β€” a pure ratio, with no units
ρ(substance)
β€” density of the substance, in kg/mΒ³ or g/cmΒ³
ρ(water)
β€” density of water, 1000 kg/mΒ³ (or 1 g/cmΒ³), in the same units as ρ(substance)

When to use it: Whenever comparing a substance's density to water's, or predicting whether it will float or sink in water.

Worked Example

Find a liquid's relative density

A liquid has a density of 800 kg/mΒ³. Find its relative density (water's density is 1000 kg/mΒ³).

    Why Does This Work?

    Because both densities are measured in the same units, those units cancel out when one is divided by the other β€” leaving a pure, unit-free number that says exactly how many times denser (or less dense) the substance is compared to water.

    Real-Life Example

    Checking car battery acid

    Mechanics used to test a lead-acid battery's charge by measuring the relative density of the acid inside it.

    As a battery discharges, the acid becomes more diluted and its relative density drops β€” a hydrometer reading of relative density was a simple, direct way to check the battery's state of charge.

    Practice

    A solid has a density of 2700 kg/mΒ³. Find its relative density.

    Medium

    Common mistake

    Giving relative density a unit (like kg/mΒ³) β€” since it is a ratio of two densities in the same units, those units always cancel, leaving a plain, unit-free number.

    Quick Review

    • RD = ρ(substance)/ρ(water) β€” no units.
    • RD > 1 means the substance sinks in water; RD < 1 means it floats.
    • Used to test the concentration or purity of liquids like battery acid and milk.
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