L-1 Units and Measurements.pdf

*** Explain the History of Measurement.
History of Measurement:
Before humans created a standardized system of measurement, many
cultures utilized local traditions for measuring objects. These are as follows:
1) The Cubit - This measurement originated in Egypt about 3000 B.C. It
was used to build pyramids.
2) The Fathom - It is a unit of length in the imperial and the U.S. customary
systems equal to 6 feet (1.8288 m).
3) The Hand-Span - It is the distance between the tip of the smallest finger
and the tip of the thumb. We still use this to measure the height of
horses.
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*** Explain space and time with different concept.
Space and time:
In science particularly in physics the concept of space and time is very important.
We need the concept of space and time to describe any event, because without it
we cannot get clear idea about space and time of the event. The concept of space
is in vogue from ancient time to locate the position of an object and space occupied
by it. Similarly the concept of time is necessary to understand sequence and
duration of the event.
Euclid’s concept:
Euclid was fast to present the geometric concept of space.
Galileo’s concept:
Galileo in his book, Statics used space and time in the law of motion and
acceleration. Thus space and time have become very important quantities in
mathematical equations.
Newton’s concept:
The concept of space and time has become more clear and taken quantitative form
through Newtonian mechanics. Space is a three dimensional extension in
Newtonian or classical physics. Space has no beginning or end. It has limitless
extension. Space can be divided into infinite small parts i.e. space is continuous.
Space is homogenous as regions of any space are identical. Space is independent.
Though all the events take place and spread within the space; space is never
influenced by any object or event. Like space, time is also independent. So,
passage of time cannot change space.

*** Why need for measurement and explain it?
Need for Measurement:
We all know that physics is a branch of science which deals with the study
of nature and natural phenomena.
Let’s say I drop a ball from a certain height; it falls freely on the
ground. Being a physics enthusiast to understand this natural phenomenon;
I will search for answers to the following questions:
1) Why did this ball fall on the ground?
2) At what speed does an object fall?
3) Is the velocity of a ball constant?
4) How much will it take for a ball to reach the ground?
5) Is the velocity of a body directly related to its mass?
To get a precise answer to these questions, measuring the quantities like
distance, velocity, and time becomes essential.

*** Explain the different types of System of Units.
A System of Units
The system of units is the complete set of units, both fundamental units, and
derived units, for all kinds of physical quantities. Each system is named with
reference to fundamental units on which it is based. The common system of
units utilized in mechanics are as follows:
1) The f.p.s or Foot-Pound System: A British engineering system of units that
uses the foot as the unit of measurement of length, and pound as the unit of
mass and second as the unit of time.
2) The c.g.s or Centimeter-Gram-Second System: A Gaussian system that
uses centimeter, gram, and second as the three basic units for length,
mass, and time respectively.
3) The M.K.S or Meter-Kilogram-Second System: The fundamental units of
length, mass, and time are meter, kilogram, and second respectively.

QUANTITY
In physics we are required to measure the physical quantities.
Accurate measurements of physical quantities are needed. Measurement
consists of the comparison of an unknown quantity with a known fixed
quantity.
Measurement is compulsory part of development technology. Accuracy of
measurement depends on
 Method of measurement.
 Measuring instrument.
Measurement consists of the comparison of given quantity with standard.
e.g. Length of table is 3 metre.
i.e. Any measurement consists of two parts.
The first is the number which indicates the magnitude of quantity and
second indicates the standard. In the above example, 3 is the magnitude and
metre is the standard (unit) of that quantity. It gives exact sense that the length
of the table is 3 times the standard.

*** Explain the physical quantities.
Physical Quantity:
A physical quantity is a quantity which can be measured (computed, quantified
or enumerated).
OR, Any quantity, which can be measured, is called a physical quantity.
Examples of physical quantities:
Length, mass, time, current, force, work, power ….. etc.
e.g. Length of table is 3 m.
Different types of quantities:
In physics, there are seven basic quantities (fundamental quantities), using
which we can derive any physical quantity.

Fundamental Quantities:
The physical quantities which do not depend on any other physical quantities for
their measurements are called fundamental quantities or base quantities.
Following are the fundamental quantities with their units and symbol of units.
Serial No. Fundamental (basic)
quantity
Fundamental
unit (S.I.)
Symbol of
unit
1 Length metre m
2 Mass kilogram Kg
3 Time second s
4 Temperature kelvin K
5 Electric current ampere A
6 Luminous intensity candela cd
7 Amount of a substance mole mol

There are two supplementary quantities (units) to fundamental quantities.
Supplementary quantity Supplementary unit Symbol of unit
1. Plane angle
2. Solid angle
radian
steradian
rad
sr
1. The Radian - It is the unit of a plane angle. One radian is the angle
subtended by the center of a circle by an arc and is equal in length to the
radius of a circle.
2. The Steradian - It is the unit of solid angle. One steradian is the solid angle
subtended at the center of a sphere, by the surface of a sphere which is
equal in area to the square of its radius.

Derived Quantities:
Physical quantities which depend on one or more fundamental quantities for
their measurements are called derived quantities.
OR, The physical quantities which are derived using one or more
fundamental quantities are called derived quantities.
Following are some derived quantities with their units and symbol of unit.
Serial
No.
Derived physical
quantity
Derived unit (S.I.) Symbol of unit
1. Area square metre m2
2. Volume cubic metre m3
3. Velocity metre/sec m/s
4. Acceleration metre/sec2 m/s2
5. Force newton N
6. Pressure newton/metre2 N/m2
7. Density kilogram/metre3 kg/m3
8. Speed metre/sec m/s
9. Work joule J

Some Definitions
Unit of length (Meter):
The distance traveled by light in vacuum (air-free space) in
1
299792458
second is
defned as one meter (m).
Unit of mass (Kilogram):
The kilogram is the mass equal to that of a cylinder made of platinum-iridium alloy
(International prototype kilogram) kept at the International Bureau of Weights and
Measures at Severs, France. The diameter of this cylinder is 3.9 cm; its height is
also 3.9 cm.
Unit of time (Second):
The time required to complete 9 192 631 770 vibrations by a caesium-133 atom is
called one second (s).
Unit of temperature (Kelvin):
The temperature which equals to
1
273.16
of the thermodynamic temperature of the
triple point of water is called one Kelvin (K).
Unit of electric current (Ampere):
The ampere is that current which produces a force of 2×10−7
Newton per meter in
vacuum between two parallel infinitely long conductors of negligible cross-sectional
area 1 meter apart when each conductor carries the same current.

Unit of luminous intensity (Candela):
Candela is the quantity of luminous intensity of any source of light which radiates
monochromatic radiation at a particular direction with a frequency of 540×1012
Hz
and emissive power of
1
683
watt per steredian solid angle.
Unit of amount of substance (Mole):
The mole is defined as the amount of substance which contains elementary
entities (e.g atoms, molecules, ions, electrons etc. or any specified group of these
particles) equal to the number of atoms in 0.012 kilogram of Carbon-12.

*** Write down the difference between fundamental quantity and derived quantity.
Difference between fundamental quantity and derived quantity:
Fundamental Quantity Derived Quantity
The quantities that do not depend on
any other physical quantity for their
measurements are known as
fundamental quantities
The products and/or ratios of the
fundamental quantities that exist in a
system of units are known as a derived
quantity
These quantities cannot be expressed
in terms of derived units
These quantities can be expressed in
terms of fundamental units
These quantities cannot be further
reduced to the elementary level
These quantities can be reduced to
their elementary level, which is
composed of fundamental units
There are only seven fundamental
units, which exist in Metric System or SI
system
There are a large number of derived
units, which exist in the Metric System
Examples:
Time (Second, s)
Length (Meter, m)
Mass (Kilogram, kg)
Temperature (Kelvin, K)
Electric current (Ampere, A)
Luminous intensity (Candela, cd)
Examples:
Heat (J)
Force (N)
Power (W)
Energy (J)
Velocity (m/s)
Density (kg/m3)

*** Explain the different types of Unit of a Physical Quantity.
Unit:
The standard used for measurement of a physical quantity is called unit of that
quantity.
Units can be classified into two groups.

Fundamental Units:
The units used to measure fundamental quantities are called fundamental units. i.e.
the unit of fundamental quantity is called fundamental unit. It does not depend on
any other unit.
There are seven fundamental (basic) physical quantities: Length, mass, time,
temperature, electric current, luminous intensity and amount of a substance and
their units are fundamental units.
Derived Units:
The units used to measure derived quantities are called derived units.
OR, The units of derived quantities which depend on fundamental units for their
measurement are called derived units.
As we have seen there are seven fundamental quantities. The remaining all
quantities are derived quantities.

*** Write down the difference between fundamental unit and derived unit.
Differences between fundamental unit and derived unit:
Fundamental Unit Derived Unit
Fundamental units are all those units
which are independent of any other unit
(including themselves).
Derived units are all those units which are
obtained by multiplying and/or dividing one
or more fundamental units with or without
introducing any other numerical factor.
Fundamental units cannot be further
reduced to elementary level; in fact,
these are elementary units.
Derived units can be reduced to its
elementary level, which are composed of
fundamental units.
Fundamental units cannot be
expressed in terms of derived units.
Derived units can be expressed in terms of
fundamental units.
Only seven fundamental units exist in
Metric System or SI system.
There exist a large number of derived units
in Metric System.
Examples of seven fundamental units,
their abbreviation and corresponding
physical properties are as follows:
 Length (Meter, m)
 Mass (Kilogram, kg)
 Time (Second, s)
 Temperature (Kelvin, K)
 Amount of substance (Mole, mole)
 Electric current (Ampere, A)
Examples of few derived units along with
corresponding physical properties are:
 Velocity (m/s)
 Acceleration (m2/s)
 Momentum (kg-m/s)
 Force (N)
 Density (kg/m3)
 Heat (J)
 Energy (J)

*** Write down the characteristics requirements of standard unit.
Requirements of standard unit:
The unit selected should have following characteristics:
1) It should be universally accepted (i.e. accepted by all).
2) It should be definite and well defined.
3) It should be invariable (fixed) with time and place.
4) It should be easily reproducible and non-perishable.
5) It should be easily comparable with other similar units.
6) Its size should be such that the quantities measured with it should not be
too large or too small.
7) It should be readily available.

*** Explain the scalar quantity and vector quantity.
Scalar Quantity:
A scalar quantity is one that has only magnitude but no direction. So, it is merely a
number accompanied by the corresponding unit. For example, length, mass,
duration, speed, etc. are scalars, so they have no direction. Scalar has no specific
direction of application, in every direction its value will be exactly the same.
The value of the scalar will be exactly the same in all directions. Therefore, every
scalar is a one-dimensional parameter. Consequently, any change in scalar
quantity reflects only change in magnitude, as no direction is associated with it.
The rules of ordinary algebra can be applied for combining scalar quantities, such
that scalars can be added, subtracted, or multiplied, in the same way, as numbers.
However, the operation of the scalar quantities with the same measurement unit
can be possible. The multiplication of two scalar quantities is known as the dot
product.

Vector Quantity:
A vector quantity has magnitude with the unit and a specific direction. So
specifying the direction of action along with its value or magnitude is mandatory
while defining or stating a vector quantity. Displacement, weight, force, velocity,
etc. are vectors.
In vector, magnitude represents the size of the quantity, which is also its absolute
value, while direction represents the side, i.e. east, west, north, south, etc. We
express vector quantities in either of the parameters i.e. one-dimensional, two-
dimensional, or three-dimensional parameters. Any change in the vector quantity
reflects either change in magnitude, change in direction, or change in both.
One can resolve Vector with the help sine or cosine of adjacent angles (vector
resolution). A vector quantity follows the triangle law of addition. The vector
product of two quantities is said to be the cross product.

*** Write down the difference between scalar quantity and vector quantity.
Parameters Scalar Vector
Meaning A scalar quantity has only magnitude,
but no direction.
Vector quantity has both magnitude and
direction.
Quantities Every scalar quantity is one-
dimensional.
Vector quantity can be one, two or
three-dimensional.
Change It changes with the change in their
magnitude
It changes with the change in their
direction or magnitude or both.
Resolution Scalar quantity cannot be resolved as
it has exactly the same value
regardless of direction.
Vector quantity can be resolved in any
direction using the sine or cosine of the
adjacent angle.
Operation Any mathematical operation carried
out among two or more scalar
quantities will provide a scalar only.
However, if a scalar is operated with
a vector then the result will be a
vector.
The result of mathematical operations
between two or more vectors may give
either scalar or vector. For example, the
dot product of two vectors gives only
scalar; while, cross product, summation,
or subtraction between two vectors
results in a vector.
Expression They are denoted by simple
alphabets, e.g. V for velocity.
They are denoted by boldface letters,
e.g. V for velocity or putting an
arrowhead over the letter.
Measurement Simple Complex
Example A car is moving at a speed of 30 Km
per hour.
A car is moving with a velocity of 30 Km
per hour in the East.

Basic Unit Conversion
Sl. No. Different Types of
Measurement
In Terms of Metre
1. 1 mm 1 x 10-3 m
2. 1 km 1 x 103 m
3. 1 inch 2.54 x 10-2 m
4. 1 foot 3048 x 10-4 m
5. 1 light year 946 x 1013 m
6. 1 mile 16 x 102 m
7. 1 angstrom 1 x 10-10 m
Measurement
In Terms of Gram
1. 1 mg 1 x 10-3 g
2. 1 kg 1 x 103 g
3. 1 stone 6.35 x 102 g
4. 1 pound 4.53 x 102 g
5. 1 ounce 0.283 x 102 g

Measurement
In Terms of Litre
1. 1 ml 1 x 10-3 l
2. 1 kl 1 x 103 l
3. 1 cubic inch 1639 x 10-5 l
4. 1 cubic foot 0.283 x 102 l
5. 1 gallon 0.03785 x 102 l
Measurement
In Terms of Joule
1. 1 kw-hr 3.6 x 106 J
2. 1 erg 1 x 10-7 J
3. 1 BTU 1.055 x 103 J
4. 1 calorie 4186 x 10-3 J
5. 1 electron volt 1.602 x 10-19 J
Measurement
In Terms of Seconds
1. 1 min 60 s
2. 1 hour 3600 s
3. 1 day 86400 s
4. 1 week 604800 s
5. 1 month 2592000 s
6. 1 year 31104000 s

L-1 Units and Measurements.pdf

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