## Measurement And Dimension Of Physical Quantity

## Measurement Of Physical Quantity

Some characteristics like smell, taste, colour, etc. of matter are subject to qualitative observations only. We use our sense organs to perceive these. On the other hand, some properties like the mass or volume of a body, the density of a matter, change in energy, etc. are subject to qualitative as well as quantitative observations.

- Measurement is an integral part of quantitative observation. Characteristics of matter or energy that can be expressed as measurable quantities are called physical quantities.
- Hence, the mass of a body is a physical quantity while its smell is not. Generally, the color of a body is not a physical quantity but when the color of light is represented by wavelength, then it is a physical quantity.
- Measurements of many physical quantities involve a measurement of time. Thus, time is also treated as a physical quantity, though time is not a direct characteristic of matter or energy.
- One of the most important targets of physics is to measure physical quantities with accuracy. Observation of a physical quantity is meaningful only when it is measured and is expressed as a numerical value with a proper unit.

**Units Of Measurement: **The result of measurement of any physical quantity is expressed in terms of its unit which is unique to that physical quantity and sets a standard for its measurement.

Any measurement is therefore written as a number of times this standard value. The standard of measurement of any physical quantity is represented by 1 and the name of the unit is

written beside 1. Therefore, the value of a physical quantity = ‘number’ ‘unit’.

**Units Of Measurement** **Example:** Suppose the length of a rod is 3 meters or 3 x 1 m. Here length is the physical quantity, meter (m) is the unit of length and the digit 3 implies that the length is 3 times the value of 1 meter (which is the standard of measurement of length).

**Read and Learn More: Class 11 Physics Notes**

To measure a physical quantity, the unit chosen should be

- Of convenient size,
- Unambiguous,
- Reproducible,
- Invariant under change of space and time and
- Acceptable to all.

**Base Or Fundamental Units And Derived Units:** There are hundreds of physical quantities in nature. Accordingly, their measurements demand hundreds of different units. If we start to assign one different unit to each of them, the entire measurement procedure will soon go beyond our control.

Fortunately, this is not actually necessary. It is observed that different physical quantities have very familiar relationships among them. As such, these units also have definite relations among them. So it is possible to

- Mark a few physical quantities that are independent of one another,
- Assign a convenient initial unit for each of them, and then
- Prepare appropriate units for all other physical quantities in terms of those initial units, using the well-known relationships among different quantities.

The initial independent units are called the base units or fundamental units and all other units structured from them are called the derived units.

- Length, mass, and time—these are three quantities entirely independent of one another. So long as our study is connected to mechanics, these three fundamental units of length, mass, and time can serve our purpose of measurement. However, these units are not sufficient for the study of the whole of physics.
- So it was decided to widen the scope of measurement by introducing some more fundamental quantities thereby increasing their number from three to seven.
- It is observed that all other physical quantities are somehow related to or can be structured from the seven base units. They are the derived units. This simplifies the measurement procedure since it is no longer necessary to create a new unit for every measurable quantity.

**Base Or Fundamental Units And Derived Units Example:** From the units of the three fundamental quantities

- Metre (m) for length,
- Kilogram (kg) for mass and
- Second (s) for time, we can structure the units of other quantities.

**A Few Examples Are Given Here:**

**Volume (V):** For a rectangular parallelepiped, volume = length x breadth x height. Actually, length, breadth, and height belonging to the same physical quantity unit of each of them is meters.

So, the unit of volume = m x m x m = m³.

**Density (ρ):** By definition, \(\rho=\frac{{mass}(m)}{\text { volume }(V)}\).

So, the unit of density = \(\frac{\mathrm{kg}}{\mathrm{m}^3}=\mathrm{kg} / \mathrm{m}^3=\mathrm{kg} \cdot \mathrm{m}^{-3}\).

**Velocity (ν):** By definition, v = \(\frac{\text { displacement }}{\text { time }}\).

Displacement is measured in units of length, i.e., meters.

So, the unit of velocity = \(\frac{m}{s}\) = m/s = m · s^{-1}.

**Systems Of Units:** A complete set of units that is used to measure all kind of fundamental and derived quantities is called a system of units. For defining the three basic units of length, mass, and time the following systems have been used :

- Centimetre-gram-second or CGS system (Metric system)
- Foot-pound-second or FPS system (Imperial system)
- Metre-kilogram-second or MKS system.

A few of the familiar derived units in the above-mentioned systems. The FPS system is almost obsolete nowadays and will not be discussed here.

**SI Units:: **If physical quantities are measured using different systems of units, the magnitudes would be different. It would become inconvenient to compare experimental results. Taking this problem into account, the International Bureau of Weights and Measures in their General Conference in 1960 introduced the International System of Units (SI).

In addition to the base units of the MKS system, this system included units of

- Temperature, kelvin or K,
- Luminous intensity, candela or cd
- Amount of substance, mole or mol and
- Electric current, ampere, or A as base units. In addition, the units of angle, (radian or rad) and solid angle, (steradian or sr) were called supplementary base units.

So, there were seven base SI units and two supplementary base units. But finally, in 1995 the supplementary units were dropped and were called derived units. SI units provide an international standard of measurement and are used widely.

Shows the base quantities and their corresponding SI base units.

**Symbol Of Units:** Each unit is conveniently assigned a sign or a symbol by which it is represented. The exact method of symbolic representation of a unit follows some internationally accepted norms. The norms, with a few examples, are :

- There is no dot (.) within the symbol or at the end.
**Example:**Centimetre: cm (not c.m or cm.)- However, if a sentence ends with a symbol then a full stop should be used to indicate the end of the sentence.

- ‘s’ or ‘es’ is not to be used in a symbol to represent the plural.
**Example:**10 g but not 10 gs.- But if the symbol is written in words and the magnitude is more than 1 (one), the plural form can be used.
**Example:**10 metres per second or 1 metre per second is quite correct whereas 10 metres/s or 10 m/seconds is wrong.

- Symbols of units named after scientists should have only the first letters in the capital.
**Example:**N for newton, A for ampere, Pa for pascal.- But if the name of the unit is written instead of the symbol, it should start with a small letter.
**Example:**newton, ampere, pascal.- The symbol of all other units starts with lowercase letters. Example: m for meter, kg for Kilogram, dyn for dyne, etc.

- The symbol of the unit should be printed in regular font, not in italics. Even when the whole sentence is written in italics, symbols must be in roman. In general, symbols of physical quantities are printed in italics, although there are exceptions.
**Example:**Representation of mass (physical quantity): m (ital), but meter (unit): m (roman).

- Multiplication and division of units follow general algebraic rules.
**Example:**10 m/s x 2s = 20 m; 20 m+2 s = 10 m/s

- A space should be inserted between two adjacent symbols to indicate multiplication. However, the use of ‘.’ or dot in that space is more common.
**Example 1:**N m or N · m. Again, to indicate division we can use the per or ‘l’ sign or the inverse power sign.**Example 2:**J/(m² · s) or J · m^{-2}· s^{-1}or \(\frac{J}{m^2 · s}\) is correct, but J/m²/s and J/m² · s are wrong.

- It is improper to use a hyphen between the numerical value and the unit when the numerical value is used as an adjective. There should be a space between the numerical value and unit symbol except in the case of superscript units for plane angle.
**Example:**16 -mm film is improper, but 16 mm film is proper.

- In thermometry, kelvin cannot be used with a degree (°) sign.
**Example:**273 K, not 273°K; but the symbols °C, °F, etc. are right.

- Sec, sq. mm, cc, mps are the wrong uses. The correct representations are s, mm² or square millimeter, cm³ or cubic centimeter, and m/s or meter per second.

While dealing with very large or very small measurements, it is convenient to express them in powers of 10. For example, 100 and 1000 can be expressed as 10² and 10³ respectively. Similarly, 1/10, 1/1000, and 1/10000 can be expressed as 10^{-1}, 10^{-3}, and 10^{-4} respectively. These are called metric prefixes. Separate names are given to these prefixes and are listed in the following table.