UNITS AND DIMENSIONS
INTRODUCTION
“MEASUREMENT” is the determination of the size or magnitude of something. Measurement can also be defined as “Comparison of an unknown quantity with some known quantity of the same kind”.
Measurement of an object consists of:
(1) The unit of measurement.
(2) The numerical value (or) Magnitude
Unit of Measurement
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity
PHYSICAL QUANTITIES:
A quantity which can be measured and by which various physical happenings can be explained and expressed in 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 cannot 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 meter means a length which is ten times the unit of length 1m. Here 10 represents the numerical value of the given quantity and meter 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
n \(\alpha {1 \over u}\)
n1u1=n2u2
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.
Examples: Mass, amount of substance, length, time, temperature, electric current, light intensity, force, velocity, density etc.