Unit of Mass - SI Unit

Unit of Mass is a standard quantity used to measure the amount of matter in an object. The SI unit of mass is kilogram (kg). Other common units of mass include the gram (g), tonne (t), pound (lb), etc. Mass plays a crucial role in our daily lives, influencing our understanding of the physical world and contributing to various scientific and practical applications.

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In this article, we will learn about mass, unit of mass in different systems, SI unit and CGS unit of mass, Conversion of mass unit, and some solved examples based on it.

Definition of Mass

Mass is the measure of the amount of matter in an object. It is an intrinsic property that is independent of an object's location and is often considered synonymous with "weight", However, weight and mass are two different physical quantities.

Mass can be categorized into different types based on the state or form of matter:

• Solid Mass: Refers to the mass of objects that maintain a fixed shape and volume, such as a book or a brick.
• Liquid Mass: Describes the mass of substances that take the shape of their container but maintain a constant volume, like water or oil.
• Gas Mass: Represents the mass of substances that conform to both the shape and volume of their container, like air or helium.

What is Unit of Mass?

The unit of mass is a measure of the amount of matter in an object. In simpler terms, Unit of mass quantifies the substance or material contained within an object. In the International System of Units (SI), the base unit of mass is the kilogram (kg).

Other common units of mass include the gram (g), metric ton (t), pound (lb), ounce (oz), and others, depending on the system of measurement being used.

Formula of Mass

The formula for mass is a measure of the quantity of matter in an object. The mass (m) is determined by

m = ρ × V

where,

• m = mass
• ρ = Density of the substance,
• V = Volume occupied by the substance.

This formula is based on the definition of density, which is the mass per unit volume of a substance.

What is 1 Kilogram?

The kilogram is the base unit of mass in the International System of Units (SI), having the unit symbol kg.

1 kg = 1000 g

SI Unit of Mass

The SI unit of mass is Kilogram. It is used universally to measure mass in scientific contexts and daily life.

SI unit of mass is the Kilogram (g).

Note: The gram is a small unit, and for larger masses, prefixes such as kilograms (kg) are commonly used.

Unit of Mass in Other Systems

While the SI system uses the kilogram as the primary unit of mass, other systems employ different units. Here are some common units and their equivalents:

System	Unit
CGS (Centimeter-Gram-Second)	Gram(g)
MKS (Meter-Kilogram-Second)	Kilogram(Kg)
Imperial System	Pounds(lb)
British Gravitational System	Slug

Some other unit of mass with their equivalent value in SI is given below:

Unit	Equivalent Value
Metric ton or Tonne (t)	1000 kg
Pound (lb)	0.4536 kg
Ounce (oz)	0.0283495 kg

Relative Mass

When the velocity (v) of the object approaches the speed of light (c), the Lorentz factor (?) increases, causing the relativistic mass (m) to increase significantly compared to the rest mass (m_o​). This phenomenon is a fundamental aspect of special relativity and is described by the formula:

m = γm_o​

where

m = relative mass of an object.

m_o = rest mass of the object.

? = Lorentz factor, which is a dimensionless quantity that depends on the object's velocity.

Unit of Relative Mass

Relative mass (m) is given by the formula m = γm_o, therefore, the unit of relative mass depends upon γ and m_o.

So, Unit of relative mass(m) = unit of γ × unit of m_o

Now, we know, γ (Lorentz factor) is dimensionless and unit of m_o is Kg

Hence, the unit of relative mass is also kg.

Conversion Between Units of Mass

The following table provides conversion factors for various mass units:

From/To	Milligram (mg)	Centigram (cg)	Decigram (dg)	Gram (g)	Decagram (dag)	Hectogram (hg)	Kilogram (kg)
Milligram (mg)	1	0.1	0.01	0.001	0.0001	0.00001	0.000001
Centigram (cg)	10	1	0.1	0.01	0.001	0.0001	0.00001
Decigram (dg)	100	10	1	0.1	0.01	0.001	0.0001
Gram (g)	1000	100	10	1	0.1	0.01	0.001
Decagram (dag)	10,000	1000	100	10	1	0.1	0.01
Hectogram (hg)	100,000	10,000	1000	100	10	1	0.1
Kilogram (kg)	1,000,000	100,000	10,000	1000	100	10	1

To convert a value from one unit to another, multiply by the corresponding factor in the table. Here are a couple of examples:

Example 1: Convert 500 grams to kilograms.

As per the table above: 1g = 0.001 kg

Therefore, 500 g = 500 × 0.001 kg = 0.5 kg

Example 2: Convert 2,500 milligrams to grams.

As per the table above: 1mg = 0.001 g

Therefore, 2500 mg = 2500 × 0.001 g = 2.5g

Read More,

• Weight and Mass
• Unit of Current
• Unit of Acceleration

Sample Problem on Unit of Mass

Problem 1. Convert 3.5 kilograms to grams.

Solution:

To convert 3.5 kilograms to grams, use the conversion factor:

1 kg = 1000 g

So, to convert 3.5 kg to g:

3.5 × 1000 = 3500g

Therefore, 3.5 kg is equal to 3500 g.

Problem 2. Convert 500 grams to kilograms.

Solution:

To convert 500 kilograms to grams, use the conversion factor:

1 kg = 1000 g i.e.,

1 g = 1 / 1000 kg

So, to convert 500 g to kg:

500 / 1000 = 0.5 kg

Therefore, 500 g is equal to 0.5 kg.

Practice Problems on Unit of Mass

Problem 1. Convert 800 grams to kilograms.

Problem 2. Convert 0.5 slugs to kilograms.

Problem 3. Convert 1200 kilograms to slugs.

Problem 4. Convert 5 slugs to grams.

Problem 5. Convert 2 kilograms to slugs.