Measurement
The process of measurement is basically a comparison process. To measure a
physical quantity, we have to find out how many times a standard amount of that
physical quantity is present in the quantity being measured. The number thus
obtained is known as the magnitude and the standard chosen is called the unit
of the physical quantity.
Unit
The unit of a physical quantity is an arbitrarily chosen standard which is
widely accepted by the society and in terms of which other quantities of
similar nature may be measured.
Standard
The actual physical embodiment of the unit of a physical quantity is known as a
standard of that physical quantity.
• To express any measurement made we need the numerical value (n) and the unit
(μ). Measurement of physical quantity = Numerical value x Unit
For example: Length of a rod = 8 m
where 8 is numerical value and m (metre) is unit of length.
Fundamental Physical Quantity/Units
It is an elementary physical quantity, which does not require any other
physical quantity to express it. It means it cannot be resolved further in
terms of any other physical quantity. It is also known as basic physical
quantity.
The units of fundamental physical quantities are called fundamental units.
For example, in M. K. S. system, Mass, Length and Time expressed in kilogram,
metre and second respectively are fundamental units.
Derived Physical Quantity/Units
All those physical quantities, which can be derived from the combination of two
or more fundamental quantities or can be expressed in terms of basic physical
quantities, are called derived physical quantities.
The units of all other physical quantities, which car. be obtained from
fundamental units, are called derived units. For example, units of velocity,
density and force are m/s, kg/m3, kg m/s2 respectively and they are examples of
derived units.
Systems of Units
Earlier three different units systems were used in different countries. These
were CGS, FPS and MKS systems. Now-a-days internationally SI system of units is
followed. In SI unit system, seven quantities are taken as the base quantities.
(i) CGS System. Centimetre, Gram and Second are used to express length, mass
and time respectively.
(ii) FPS System. Foot, pound and second are used to express length, mass and
time respectively.
(iii) MKS System. Length is expressed in metre, mass is expressed in kilogram and
time is expressed in second. Metre, kilogram and second are used to express
length, mass and time respectively.
(iv) SI Units. Length, mass, time, electric current, thermodynamic temperature,
Amount of substance and luminous intensity are expressed in metre, kilogram,
second, ampere, kelvin, mole and candela respectively.
Definitions of Fundamental Units
Supplementary
Units
Besides the above mentioned seven units,there are
two supplementary base units. these are (i) radian (rad) for angle, and (ii)
steradian (sr) for solid angle.
Advantages
of SI Unit System
SI Unit System has following advantages over the
other Besides the above mentioned seven units, there are two supplementary base
units. These are systems of units:
(i) It is internationally accepted,
(ii) It is a rational unit system,
(iii) It is a coherent unit system,
(iv) It is a metric system,
(v) It is closely related to CGS and MKS systems of units,
(vi) Uses decimal system, hence is more user friendly.
Other Important Units of Length
For measuring large distances e.g., distances of planets and stars etc., some
bigger units of length such as ‘astronomical unit’, ‘light year’, parsec’ etc.
are used.
• The average separation between the Earth and the sun is called one
astronomical unit.
1 AU = 1.496 x 1011 m.
• The distance travelled by light in vacuum in one year is called light year.
1 light year = 9.46 x 1015 m.
• The distance at which an arc of length of one astronomical unit subtends an
angle of one second at a point is called parsec.
1 parsec = 3.08 x 1016 m
• Size of a tiny nucleus = 1 fermi = If = 10-15 m
• Size of a tiny atom = 1 angstrom = 1A = 10-10 m
Parallax Method
This method is used to measure the distance of planets and stars from earth.
Parallax. Hold a pen in front of your eyes and look at the pen by closing the
right eye and ‘ then the left eye. What do you observe? The position of the pen
changes with respect to the background. This relative shift in the position of
the pen (object) w.r.t. background is called parallax.
If a distant object e.g., a planet or a star subtends parallax angle 0 on an
arc of radius b (known as basis) on Earth, then distance of that distant object
from the basis is given.
• To estimate size of atoms we can use electron microscope and tunneling
microscopy technique. Rutherford’s a-particle scattering experiment enables us
to estimate size of nuclei of different elements.
• Pendulum clocks, mechanical watches (in which vibrations of a balance wheel
are used) and quartz watches are commonly used to measure time. Cesium atomic
clocks can be used to measure time with an accuracy of 1 part in 1013 (or
to a maximum discrepancy of 3 ps in a year).
• The SI unit of mass is kilogram. While dealing with atoms/ molecules and
subatomic particles we define a unit known as “unified atomic mass unit” (1 u),
where 1 u = 1.66 x 10-27 kg.
For this 1 cm3 of oleic acid is dissolved in alcohol to
make a solution of 20 cm3. Then 1 cm3 of this solution is taken and diluted to 20
cm3, using alcohol. So, the concentration of the
solution is as follows:
`\left ( \frac{1}{20x20} \right )cm^{3}`
