**Category : **JEE Main & Advanced

A quantity which can be measured and by which various physical happenings can be explained and expressed in the form of laws is called a physical quantity. For example length, mass, time, force etc.

On the other hand various happenings in life e.g., happiness, sorrow etc. are not physical quantities because these can not be measured.

Measurement is necessary to determine magnitude of a physical quantity, to compare two similar physical quantities and to prove physical laws or equations.

A physical quantity is represented completely by its magnitude and unit. For example, 10 metre means a length which is ten times the unit of length. Here 10 represents the numerical value of the given quantity and metre represents the unit of quantity under consideration. Thus in expressing a physical quantity we choose a unit and then find that how many times that unit is contained in the given physical quantity, i.e.

Physical quantity (Q) = Magnitude × Unit = n × u

Where, n represents the numerical value and u represents the unit. Thus while expressing definite amount of physical quantity, it is clear that as the unit(u) changes, the magnitude(n) will also change but product 'nu' will remain same.

i.e. n u = constant, or \[{{n}_{1}}{{u}_{1}}={{n}_{2}}{{u}_{2}}=\text{constant}\]; \ \[n\propto \frac{1}{u}\]

i.e. magnitude of a physical quantity and units are inversely proportional to each other. Larger the unit, smaller will be the magnitude.

**(1) Ratio (numerical value only) :** When a physical quantity is the ratio of two similar quantities, it has no unit. e.g. Relative density = Density of object/Density of water at 4oC Refractive index = Velocity of light in air/Velocity of light in medium Strain = Change in dimension/Original dimension

**(2) Scalar (magnitude only) :** These quantities do not have any direction e.g. Length, time, work, energy etc. Magnitude of a physical quantity can be negative. In that case negative sign indicates that the numerical value of the quantity under consideration is negative. It does not specify the direction. Scalar quantities can be added or subtracted with the help of ordinary laws of addition or subtraction.

**(3) Vector (magnitude and direction) :** These quantities have magnitude and direction both and can be added or subtracted with the help of laws of vector algebra e.g. displacement, velocity, acceleration, force etc.

*play_arrow*Physical Quantity*play_arrow*Fundamental and Derived Quantities*play_arrow*Fundamental and Derived Units*play_arrow*S.I. Prefixes*play_arrow*Standards of Length, Mass and Time*play_arrow*Practical Units*play_arrow*Dimensions*play_arrow*Quantities Having same Dimensions*play_arrow*Important Dimensions of Complete Physics*play_arrow*Application of Dimensional Analysis*play_arrow*Limitations of Dimensional Analysis*play_arrow*Significant Figures*play_arrow*Rounding Off*play_arrow*Significant Figures in Calculation*play_arrow*Order of Magnitude*play_arrow*Errors of Measurement*play_arrow*Propagation of Errors

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