INTRODUCTION
• Basic physics is a branch of science which deals with the
study of matter and its properties.
• Measurable property of matter is called a physical quantity.
• Measurement of these Quantities is important and has
numerous applications in industry, construction and other field
of engineering and technology.
• In this chapter we will study about few Physical Quantities, their
units and measurements and errors in the measurement.
Fundamental Physical Quantities
❑ Physical quantities which are independent (base) and does
not depend on any other physical quantities are called
Fundamental Physical Quantities.
❑ Length, Mass and Time are taken as the basic fundamental
quantities in mechanics.
❑ Other fundamental physical quantities are electric current,
temperature, luminous intensity and amount of substance.Derived Physical Quantities
❑ Physical quantities which can be expressed in terms of (base)
fundamental physical quantities are called Derived Physical
Quantities.
❑ All physical quantities other than fundamental physical
quantities can be expressed in terms of fundamental ones.
e.g. speed = distance/time
❑ Hence speed depends on distance and time. Similarly,
area, density, power, force, energy etc. can be
expressed in terms of fundamental quantities and so
they are derived quantities.
Physical Quantity
• A quantity which is measurable is called Physical Quantity.
• As we are aware there are two types of mathematical
physical quantity viz; scalar and vector.
• According to the nature and existence of the physical
quantities, they are classified as-
1. Fundamental Physical Quantity
2. Derived Physical QuantityRequirement of
Standard Units
• Requirement of standard unit are as follows:
– It should be universally accepted (i.e. accepted by all).
– It should be definite and well defined.
– It should be invariable (fixed) with time and place.
– It should be easily reproducible.
– It should be easily comparable with other similar units.
– Its size should be such that the quantities measured with it
should not be too large or too small.
– It should be readily available
Fundamental & Derived Units
• The units of fundamental physical quantities are called fundamental units.
• The units of the fundamental or base quantities are called
fundamental or base units
– Examples of fundamental units: metre, kilogram, second, etc.
• The units of derived physical quantities are called derived
units.
• The units of the derived quantities which can be expressed from the
base or fundamental quantities are called derived units.
– Examples of derived units: metre/sec, kg/m3
, kg m/s2
, kg m2
/s2
, etcUnits
• The standard used for the measurement of physical quantity is called its unit.
• For example, take the case of length and distance.
– To measure the distance of stars we use the unit light year
which is the distance travelled by the light in one year and is
equal to 9.46 x 1012 km.
– To measure the distance of a place we use kilometers.
– To measure the length or size of an object we may use meter,
centimeter or millimeter.
– To measure the wavelength of light we use Angstrom unit,
where 1A° = 10-10 m.British System
• British System:
In British system the basic unit of length,
mass and time are Foot, Pound and Second (F.P.S.) respectively.
• In British system, conversion to sub-units is complicated.
• Again different physical quantities are measured in different
sub-units.
• Hence British system is not commonly used for the measurement of the physical quantities.Metric System
• Metric System: Metric system is the French system of units.
In this system the different sub units are given as powers of ten. C.G.S. and M.K.S. are the sub-systems of the metric
system of units.
– C.G.S. system: In this system length is measured in
centimeter, mass in gram and time in second.
– M.K.S. system: In this system length is measured in
meter, mass in kilogram and time in second.System of Units
• Length, Mass and Time are taken as basic fundamental
quantities and their units are used to express different
systems of unit.
– British System (F.P.S)
– Metric System (C.G.S, M.K.S)
– Système Internationale (S.I)Errors
• The difference between the actual value (true value of
mean value) and measured value is called errors.
• An error is a fault or uncertainty, which may occur even in the
most careful observation while taking measurement by an
instrument.
• Errors are classified as –Instrumental Errors
• The errors caused due to use of faulty instruments are called
instrumental errors.
• The error remains the same for any measurement and so is called
constant error.
• Such errors may be due to faulty construction or inappropriate
calibration of instrument.
• Zero error is an example of instrumental error.
• If Vernier caliper has zero error or not calibrated properly then each
measured value will give same error.
• Such errors can be eliminated by taking the same measurement
with the help of different instruments.Système Internationale (S.I)
• SI System: Before 1960, different countries were using different
systems of units.
• Hence Scientists and Engineers had the difficulty of
understanding and conversion of different systems of units.
• To overcome this difficulty in 1960, the General Conference of
Weights and Measures decided to follow the same system of
unit throughout the world.
• This system of unit is called International System (SI) of units.
Note: M.K.S. System is more or less the same as the SI
system.
Systematic Errors
• Errors caused by virtue of certain definite rule or known causes
are called systematic error.
• Systematic errors are caused due to the defective setting or
adjustment of the instruments by the experimenter.
– If the pointer of a magnetic compass is not pivoted at the center of
the magnetic scale, a systematic error will occur
– This error may be due to a defective alignment of the instrument
by observer. e.g. Zero error.
– This error can be caused due to some personal habit of the
observer. e.g. Parallax error.
– The error due to imperfect experimental arrangement. e.g. radiation in calorimeter experiments.
• As this errors are persistent and related to personal cause it is
also called persistent error or personal error.Minimization of Errors
• The errors in any observation can be minimized
by adopting the following steps.
– taking large magnitude of the quantity to be measured.
– consider mean value by taking multiple readings.
– using smallest least count instrument.
Random Errors
• The errors caused due to sudden change in experimental
conditions is called random errors.
• These error cannot be controlled and hence it is also called as
accidental errors.
• Same person may get different readings because of human
limitations, then the error caused is called random error.
• Errors caused due to change in temperature or pressure,
change in humidity, fluctuation in voltage, etc. are examples of
random error.Estimation of Errors
Let x be the true or correct or average or mean value and x_{1} be the measured value of the physical quantity to be measured.
Errors in any measurement can be represented by the following ways
Absolute error: The difference between the magnitude of true value and measured value is called the absolute error.
Absolute error Ax =| overline x - x_{i} |
Average absolute error: The average of all absolute error in a measurement is called mean or average absolute error.
Average absolute errorAccuracy, Precision & Significant Figure
• Accuracy is agreement of the measured value with the true
value of the measured quantity.
• Precision is defined as the repeatability of a measuring
process.
• Significant figure is defined as a figure in any place (in
number) which is reasonably trustworthy or meaningful.
– It indicates the number of digits in which we have confidence in
respect to its accuracy.
– The greater the number of significant features, the more
accurate is the measurement.
– If the length of an object measured by a meter scale is 25.8 cm.
The corresponding significantRules and identification of S.F
• All non-zero digits are considered significant.
– For example, 91 has two significant figures (9 and 1), while 123.45 has five
significant figures (1, 2, 3, 4 and 5).
• Zeros between any two non-zero digits are significant.
– Example: 101.1203 has seven significant figures: 1, 0, 1, 1, 2, 0 and 3.
• Zeros before non-zero digits are not significant.
– For example, 0.00052 has two significant figures: 5 and 2.
• Zeros behind non-zero digit in a number with decimal point are
significant.
– For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number
0.000122300 still has only six significant figures (the zeros before the 1 are not
significant).Quantities with same
Dimensional formulae
1. Impulse and momentum
2. Work, energy, torque, moment of force
3. Angular momentum, Planck’s constant, rotational impulse
4. Stress, pressure, modulus of elasticity, energy density
5. Force constant, surface tension, surface energy
6. Angular velocity, frequency, velocity gradient
7. Gravitational potential, latent heat
8. Thermal capacity, entropy, universal gas constant and
Boltzmann’s const.
9. Force, thrust
10. Power, luminous flux
