CBSE Class 11 Physics Units Dimensions Vectors Exam Notes

UNITS AND DIMENSIONS

In order to measure a physical quantity, it has to be expressed in terms of a certain reference standard of measurement of that physical quantity which is called a unit. The magnitude of physical quantity is expressed in terms of the number of times the physical quantity contains that unit. The basic physical quantities, which do not depend upon other quantities, are known as the fundamental quantities. Mass, length and time are considered as fundamental quantities. The units which can be derived from the fundamental units are known as derived units. In mechanics, all quantities can be expressed in terms of mass, length and time. The main systems of units are given as follows :
1. C.G.S. or Centimetre, Gram, Second System.
2. F .P.S. or Foot, Pound, Second System.
3. M.K.S. or Metre, Kilogram, Second System.
4. S.I. System : These are seven basic or fundamental quantities in the international system of units called S.I. System which can express all physical quantities including heat, optics and electricity and magnetism. These basic seven quantities with their units and symbols are given as follows :
S.No.           Physical Quantity              S.I.                     Unit Symbol
1.                 Mass                                   Kilogram                Kg
2.                 Length                                Metre                     m
3.                 Time                                   Second                   s
4.                 Temperature                       Kelvin                     K
5.                 Luminous                           Intensity Candela    Cd
6.                Electric Current                Ampere                    A
7.                Amount of Substance       Mole                       mol.
Also, two supplementary units are used as radian (rad) for plane angle and steradian (sr) for solid angle.
The above mentioned International System of Units (S.I.) are now extensively used for the scientific measurements.
The following practical units are conveniently used and are expressed in terms of S .I. system of units also.

1. Micron is a small unit for measurement of length. 1 micron = 1 μm = 10^–6m

2. Angstrom is a unit of length in which the size of atom is measured and is used in Atomic Physics. 1 Angstrom = 1 Å = 10^–10 metre

3. Light Year is a unit of distance travelled by light in free space and is used in Astrophysics. 1 Light Year = 3 × 10⁸ m/s × 365 × 24 × 60 × 60 = 9.5 × 10¹⁵ metres

4. Fermi is a unit of distance in which the size of a nucleus is measured. 1 Fermi = 10^–15m

5. Atomic Mass Unit : It is a unit of mass equal to 1/12 th of mass of Carbon - 12 nucleus and is used in measuring the masses of nuclei. 1 atomic mass unit ~ 1.67 × 10^–27 kg.

DIMENSIONS
The dimensions of a derived unit is defined as the power to which the fundamental units of mass, length and time should be raised to represent that physical quantity. The expression which represents the dimension of a physical quantity is called the dimensional formula which is given as [Ma Lb Tc] where a, b and c are respective dimensions of mass, length and time. For example, the dimensional formula for volume = [L³], velocity = [LT^–1], Power = [ML²T^–2] etc.