# Unit & Dimension, Measurement

## Physical Quantities

The quantities by means of which we describe the laws of physics are called Physical Quantities.

The ‘Standared’ of measurement of a physical quantity is called the unit of that physical quantity.

The magnitude of physical quantity = NU, where

N = Numerical value of the measure of the quantity and

U = Unit of the quantity.

The Unit of length, mass and time are called fundamental units. The units of other quantities which are derived from mass, length and time are called derived units.

System of Units : The common system of units are :

- FPS system : The units of length, mass and time are respectively foot, pound and second.
- CGS system : The units of length, mass and time are respectively centimetre, gram and second.
- MKS system : The units of length, mass and time are respectively metre, kilogram and second.
- The International system of units (SI units).

By international agreements the seven base units of the S.I. system are :

- The metre (
*m*) ------- Standard of length. - The kilogram (
*kg*) ------- Standard of mass. - The second (
*s*) ------- Standard of time. - The kelvin (
*K*) ------- Standard of temperature. - The candela (
*cd*) ------- Standard of luminous in intensity. - The mole (
*mol*) ------- Standard of amount of substance. - The ampere (
*A*) ------- Standard of electric current.

In addition to this there are two supplementary SI Units :

- Radian for plane angle.
- Steradian for solid angle.

Radian and degree are the Units of angle.

### Dimensions

Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised to represent the given physical quantity. In mechanics all physical quantities can be expressed in terms of mass (M), length (L) and time (T).

Example : Force = mass x acceleration = Or,

So, the dimensions of force are 1 in mass, 1 in length and – 2 in time.

#### Dimensionless quantity

In the equation then the quantity is called dimensionless.

Examples : Strain, specific gravity, angle. They are ratio of two similar quantities.

A dimensionless quantity has same numeric value in all system of units.

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Unit, Dimension and Measurement -Uses of Dimensional equation-For IIT, NIT and all other Engineering Entrance Test