How to Convert Between SI and CGS Units of Density with Examples
Density is an important concept in Physics that refers to the amount of mass present within a specific volume of a substance. Simply put, it measures how much matter is packed into a given space. This property is fundamental for understanding the behavior of solids, liquids, and gases in various scientific and real-world applications.
The formula for density is straightforward. It is defined as the mass (M) of a substance divided by its volume (V). This relationship is written as:
Density (d) = Mass (M) / Volume (V)
Density is commonly represented by the symbol "d." In calculations, always ensure that the units for mass and volume are consistent, as this affects the final unit of density.
Different systems use specific units for expressing density. The most widely used unit, especially in basic science and laboratory contexts, is the gram per cubic centimeter (g/cm³).
Understanding the Units of Density
Choosing the correct unit for density depends on the measurement system:
| System | Unit Name | Symbol | Typical Use |
|---|---|---|---|
| CGS (Centimeter-Gram-Second) | Gram per cubic centimeter | g/cm³ | Lab measurements, Chemistry, Introductory Physics |
| SI (International System) | Kilogram per cubic meter | kg/m³ | Physics, Engineering |
For many practical cases, the density of water is used as a reference. Water has a density of 1 g/cm³ in the CGS system. This means 1 cubic centimeter of water has a mass of 1 gram. In the SI system, this is equivalent to 1000 kg/m³.
Density Calculation: Step-by-Step Example
Let's see how to use the density formula to solve a typical problem.
| Problem | Calculation Steps | Answer |
|---|---|---|
| A sample has a mass of 20 g and a volume of 5 cm³. Find its density. |
Step 1: Use the formula d = M / V Step 2: M = 20 g, V = 5 cm³ Step 3: d = 20 g / 5 cm³ |
d = 4 g/cm³ |
This calculation shows that a 20 gram sample spread out over 5 cubic centimeters has a density of 4 grams per cubic centimeter.
Standard Density Values
| Substance | Density (g/cm³) | Remarks |
|---|---|---|
| Water | 1.0 | At standard conditions |
| Lead | 11.3 | Very dense metal |
| Air | 0.0012 | Much less dense than solids and liquids |
Various materials can be compared using density. Solids like lead have much higher densities than liquids such as water. Gases like air are the least dense.
Key Points to Remember
- Density describes how much matter exists in a particular volume.
- The formula is density = mass / volume.
- The most common unit is gram per cubic centimeter (g/cm³).
- Water is used as a standard reference, with a density of 1 g/cm³.
Knowing how to calculate and compare densities is essential in Physics and Chemistry. It helps explain why some objects float, others sink, and why materials have different properties.
Next Steps for Further Learning
- Practice calculations using the mass and volume of different substances.
- Explore how density affects the behavior of gases, liquids, and solids.
- Visit Unit of Density on Vedantu for more examples and topic explanations.
- Try solving real-world density questions from previous Physics exams.
For more detailed explanations and practice questions on density and other Physics concepts, visit our Physics topic pages. Build your confidence through step-by-step problem solving and clear conceptual summaries.
FAQs on Unit of Density: SI and CGS Units, Formula, Examples
1. What is the SI unit of density?
The SI unit of density is kilogram per cubic metre (kg/m3). This means density is calculated as mass (in kilograms) divided by volume (in cubic metres). It is the standard unit used in Physics, engineering, and competitive exams.
2. What is the CGS unit of density?
The CGS unit of density is gram per cubic centimetre (g/cm3). This unit is widely used in Chemistry laboratory work and smaller-scale scientific measurements.
- 1 g/cm3 = 1000 kg/m3
- Used frequently for density values of water and other liquids
3. How is density defined in Physics?
Density is defined as the mass per unit volume of a substance.
- Formula: ρ = m / V
- ρ (rho): Symbol for density
- m = mass, V = volume
4. What is the formula for density?
The formula for density is:
Density (ρ) = Mass (m) / Volume (V)
- Mass should be in kg (SI) or g (CGS)
- Volume should be in m3 (SI) or cm3 (CGS)
5. What are the common units of density used in Physics?
Common units of density include:
- SI Unit: kg/m3
- CGS Unit: g/cm3
- English System: lb/ft3 (pound per cubic foot)
6. How do you convert density from SI to CGS units or vice versa?
To convert:
- From SI to CGS: 1 kg/m3 = 0.001 g/cm3
- From CGS to SI: 1 g/cm3 = 1000 kg/m3
- Multiply or divide by 1000 as per the conversion required.
7. What is the density of water in SI and CGS units?
The density of pure water at 4°C is:
- SI: 1000 kg/m3
- CGS: 1 g/cm3
8. What is relative density and its unit?
Relative density is the ratio of the density of a substance to the density of water.
- Formula: Relative Density = Density of substance / Density of water
- Unit: It is dimensionless (no unit)
9. Why is understanding density units important in competitive exams?
Knowing correct density units helps avoid calculation errors and is essential for:
- Accurate unit conversions
- Solving Physics numericals in IIT-JEE, NEET, and board exams
- Gaining conceptual clarity in both Physics and Chemistry
10. Can you give a solved example to calculate density?
Example: A block has a mass of 250 g and volume 200 cm3.
- Density (ρ) = m / V = 250 g / 200 cm3 = 1.25 g/cm3
11. What is the symbol for density?
The symbol for density is the Greek letter "rho" (ρ). This standard notation is used in all Physics and Chemistry formulas involving density.
12. Where is the unit of density applied in real life?
Density units are used in:
- Identifying substances in lab and industry
- Calculating buoyancy or flotation
- Material selection in manufacturing
- Petroleum and chemical industries
- Everyday objects' quality and purity tests
