This document discusses units and measurements. It covers the International System of Units (SI) which has seven fundamental units (meter, kilogram, second, kelvin, ampere, mole, candela) and two supplementary units (radian, steradian). It describes rules for writing SI units and provides examples of common prefixes used with units. It also discusses dimensional analysis and provides examples of deriving physical quantities and checking the dimensional correctness of equations. Finally, it lists some practical units used for measuring length, area, mass, time and compares the sizes of different units used in everyday life versus scientific and astronomical contexts.

1. UNITS AND
MEASUREMENTS
C H A P T E R - I I

2. • 2a. System of Units
– Need for Measurement: Units of Measurements of system of Units, SI units,
Fundamental and derived units.
• 2b. Length, Mass and Time Measurements
– Length, Mass and Time measurements
• 2c. Significant Figures and Error Analysis
– Accuracy and precision of Measuring Instruments; Errors in Measurements;
Figures.
• 2d. Dimensional Analysis
– Dimensions of Physical quantities, dimensional analysis and its applications.

3. MEASUREMENT IN EVERYDAY LIFE
MEASURMENT OF MASS MEASURMENT OF VOLUME
MEASUREMENT OF LENGTH MEASUREMENT OF

4. NEED FOR
MEASUREMENT IN
PHYSICS• To p e r f o r m e x p e r i m e n t s
• E x p e r i m e n t s r e q u i r e m e a s u r e m e n t s ,
a n d w e m e a s u r e s e v e r a l p h y s i c a l
p r o p e r t i e s l i k e l e n g t h , m a s s , t i m e ,
t e m p e r a t u r e , p r e s s u r e e t c
• E x p e r i m e n t a l v e r i f i c a t i o n o f l a w s &
t h e o r i e s a l s o n e e d s m e a s u r e m e n t o f
p h y s i c a l p r o p e r t i e s .

5. PHYSICAL QUANTITY
• A physical property that can be measured and described by a number is called
physical quantity.
• Examples:
• Mass of a person is 65 kg.
• Length of a table is 3 m.
• Area of a hall is 100 m2 .
• Temperature of a room is 300 K
TYPES OF PHYSICAL QUANTITY
1. FUNDAMENTAL QUANTITIES
1. DERIVED QUANTITIES

6. FUNDAMENTAL QUANTITIES
&
DERIVED QUANTITIES
Fundamental quantities :
The physical quantities which do not depend on any other physical
quantities
for their measurements are known as fundamental quantities.
• Examples:
• Mass • Length • Time • Temperature
Derived quantities :
The physical quantities which depend on one or more fundamental
quantities
for their measurements are known as derived quantities.
Examples:
• Area • Volume • Speed • Force

7. UNITS FOR MEASUREMENT
• The standard used for the measurement of a physical quantity is called a unit.
• Examples:
• meter, foot, inch for length
• kilogram, pound for mass
• second, minute, hour for time
• Fahrenheit, kelvin for temperature
Characteristics of units
• Well defined
• Suitable size
• Reproduceable
• Invariable
• Internationally acceptable

8. SYSTEM OF UNITS
•CGS system of units : -
– This system was first introduced in
France.
– It is also known as Gaussian system of
units.
– It is based on centimeter, gram and
second as the fundamental units of
length, mass and time respectively.

9. MKS SYSTEM OF UNITS
•This system was also introduced in France.
• It is also known as French system of units.
• It is based on meter, kilogram and second
as the fundamental units of length, mass
and time respectively.

10. FPS SYSTEM OF UNITS
•This system was introduced in Britain.
• It is also known as British system of units.
• It is based on foot, pound and second as
the fundamental units of length, mass and
time.

11. INTERNATIONAL SYSTEM OF UNITS (SI)
• In 1971, General Conference on Weight and
Measures held its meeting and decided a system of
units for international usage.
• This system is called international system of units and
abbreviated as SI from its French name.
• The SI unit consists of seven fundamental units and
two supplementary units.

12. SEVEN FUNDAMENTAL UNITS
FUNDAMENTAL
QUANTITY
SYMBOL
SI UNIT SYMBOL Definition
Length meter m The meter is the length of the path travelled by light in
vacuum during a time interval of 1/299,792,458 of a
second
Mass kilogram kg The kilogram is the mass of prototype cylinder of
platinum-iridium alloy preserved at the International
Bureau of Weights and Measures, at Sevres, near
Paris.
Time second s One second is the time taken by 9,19,26,31,770
oscillations of the light emitted by a cesium–133 atom.
Temperature kelvin K The kelvin, is the fraction 1/273.16 of the
thermodynamic temperature of the triple point of water
Electric current ampere A The ampere is that constant current which, is
maintained in two straight parallel conductors of infinite
length, of negligible circular cross – section, and placed
1 meter apart in vacuum, would produce between these
conductors a force equal to 2x10-7 newton per meter of
length.
Luminous intensity candela Cd The candela is the luminous intensity, in a given
direction, of a source that emits monochromatic
radiation of frequency 540x1012 hertz and that has a
radiant intensity in that direction of 1/683 watt per
steradian.
Amount of substance mole mol The mole is the amount of substance os a system,

13. TWO SUPPLEMENTARY UNITS
RADIAN: A radian is the measure
of an angle that, when drawn as
a central angle, subtends an arc
whose length equals the length
of the radius of the circle. ( To
m e a s u r e p l a n e a n g l e ) Symbol :rad
STERADIAN: Unit for solid angle is
steradian. I.e. to measure solid angle.
Symbol: sr

14. RULES FOR WRITING SI UNITS
1
• Full name of unit always starts with small letter even if named after a person.
newton not as Newton
ampere not as Ampere
coulomb not as Coulomb
2
– Symbol for unit named after a scientist should be in capital letter.
N for newton
K for kelvin
A for ampere
C for coulomb

15. RULES FOR WRITING SI UNITS
3
• Symbols for all other units are written in small letters.
m for meter
s for second
kg for kilogram
cd for candela
4
• One space is left between the last digit of numeral and the symbol of a
unit.
10 kg not 10kg
5 N not 5N
15 m not 15m

16. RULES FOR WRITING SI UNITS
5. The units do not have plural forms.
6 meter not 6 meters
14 kg not 14 kgs
20 second not 20 seconds
18 kelvin not 18 kelvins
6. Full stop should not be used after the units.
7 meter not 7 meter.
12 N not 12 N.
25 kg not 25 kg.
7. No space is used between the symbols for units.
4 Js not 4 J s
19 Nm not 19 N m
25 VA not 25 V A.

17. NEGATIVE POWERS OF 10
S.No Prefix Symbol Multiplier
factor
Power of 10
1 yocto y 10-24 -24
2 zepto z 10-21 -21
3 atto a 10-18 -18
4 femto f 10-15 -15
5 pico p 10-12 -12
6 nano n 10-9 -9
7 micro µ 10-6 -6
8 milli m 10-3 -3
9 centi c 10-2 -2
10 deci d 10-1 -1

18. POSITIVE POWERS OF 10
S.No Prefix Symbol Multiplier
factor
Power of 10
1 yotta Y 1024 24
2 zetta Z 1021 21
3 exa E 1018 18
4 peta P 1015 15
5 tera T 1012 12
6 giga G 109 9
7 mega M 106 6
8 kilo m 103 3
9 hecto k 102 2
10 deca da 101 1

19. USE OF SI PREFIXES
• 3 milliampere = 3 mA = 3 x 10−3 A
• 5 microvolt = 5 μV = 5 x 10−6 V
• 8 nanosecond = 8 ns = 8 x 10−9 s
• 6 picometre = 6 pm = 6 x 10−12 m
• 5 kilometre = 5 km = 5 x 103 m
• 7 megawatt = 7 MW = 7 x 106 W

20. DERIVED QUANTITIES AND THEIR UNITS
The physical quantities which depend on one or more fundamental quantities
for their measurements are known as derived quantities.

21. •Part 2

22. https://www.bing.com/videos/search?view=detail&mid=47162869C7F0DA0E9EB747162869C7F0DA0E9EB7&shtp=LinkedIn&shid=6193efde-2136-442e-9077-
d1e728ada896&shtk=VW5pdmVyc2UgU2l6ZSBDb21wYXJpc29uIDNE&shdk=U2l6ZSBjb21wYXJpc29uIG9mIHRoZSBlbnRpcmUgdW5pdmVyc2UgMjAxNyBpbiAzRC4gRnJvbSB0aGUgZmFicmljIG9mIHNwYWNlLXRpbWUgaXRzZWxmLCB3ZSBqb3VybmV5IG91dHdhcmRzIHRvIHN1YmF0b21pYyBlbGVtZW50YXJ5IHBhcnRpY2xlcywgdG8gYXRvbXMsIG1
vbGVjdWxlcywgdmlydXNlcywgYmFjdGVyaWEsIGNlbGxzLCBhbmltYWxzLCBwbGFuZXMsIHNoaXBzLCBidWlsZGluZ3MsIG1vdW50YWlucywgY291bnRyaWVzLCBtb29ucywgcGxhbmV0cywgc3RhcnMsIHNvbGFyIHN5c3RlbXMsIGJsYWNrIGhvbGVzLCBuZWJ1bGFzLCBnYWxheGllcywgc3VwZXJjbHVzdGVycywgc3VwZXJjbHVzdGVyLWNvbXBsZXggYW
5kIGZpbmFsbHkgdGhlIHVuaXZlcnNlLCBidXQgaXQgZ29lcyBiZXlvbmQgdGhhdC4uLiBUaGFua3MgZm9yIGV2ZXJ5b25lJ3Mgc3VwcG9ydCB0aGF0IHdlJ3ZlIG1hbmFnZWQgdG8gaGl0IDEwMEsgc3Vic2NyaWJlcnMgKGFjdHVhbGx5IDEyNUsuLi4%3D&shhk=rtDse44IgnTpx3J7Q1ZL0K2WqCliNhVzQmuusF4wNoY%3D&form=VDSHOT&shth=OSH.o7wwxiK
5t36pbiFUXiohZg

23. SOME PRACTICAL UNITS FOR MEASURING LENGTH
1 micron = 10−6 m Molecules 1 nanometer = 10−9 m
Atom 1 angstrom = 10−10 m
Bacteria
Nucleus 1 fermi = 10−15 m

24. ASTRONOMICAL UNIT = IT IS DEFINED AS THE MEAN DISTANCE
OF THE EARTH FROM THE SUN.
• 1 ASTRONOMICAL UNIT = 1.5 X 1011 M
Distance of

25. Light year = it is the distance travelled by light in vacuum in one
year.
• 1 light year = 9.5 x 1015 m
Distance of stars

26. PARSEC = IT IS DEFINED AS THE DISTANCE AT WHICH AN ARC OF 1 AU
SUBTENDS AN ANGLE OF 1’’.
• IT IS THE LARGEST PRACTICAL UNIT OF DISTANCE USED IN ASTRONOM Y.
• 1 PARSEC = 3.1 X 1016 M

27. SOME PRACTICAL UNITS FOR MEASURING AREA
• Acre = It is used to measure large areas in British system of
units.
1 acre = 208’ 8.5” x 208’ 8.5” = 4046.8 m2
• Hectare = It is used to measure large areas in French system
of units.
1 hectare = 100 m x 100 m = 10000 m2 •
Barn = It is used to measure very small areas, such as nuclear
cross sections.
1 barn = 10−28 m2

28. SOME PRACTICAL UNITS FOR MEASURING MASS
Steel Bar 1 metric ton – 1000 kg Grains 1 quintal = 100 kg
New born babies 1 pound = 0.454 kgCrops 1 slug = 14.59 kg

29. 1 CHANDRASEKHAR LIMIT = 1.4 X MASS OF SUN = 2.785 X 1030 KG
• IT IS THE BIGGEST PRACTICAL UNIT FOR MEASURING MASS.
Massive black holes

30. •1 atomic mass unit = 1 /12 x mass of single
C
atom
• 1 atomic mass unit = 1.66 x 10−27 kg
• It is the smallest practical unit for
measuring
mass.
• It is used to measure mass of single

31. SOME PRACTICAL UNITS FOR MEASURING TIME
• 1 Solar day = 24 h
• 1 Sidereal day = 23 h & 56 min
• 1 Solar year = 365 solar day = 366 sidereal day
• 1 Lunar month = 27.3 Solar day
• 1 shake = 10−8 s

32. SEVEN DIMENSIONS OF THE WORLD
Fundamental quantities
Dimensions
Length [L]
Mass [M]
Time [T]
Temperature [K]
Current [A]
Amount of substance [N]
Luminous intensity [ J ]

33. DIMENSIONS OF A PHYSICAL QUANTITY
The powers of fundamental quantities in a derived quantity
are called dimensions of that quantity.

34. DIMENSIONS OF A PHYSICAL QUANTITY
• Example:
Density = Mass
Volume
= Mass
length x breath x height
[Density] = [M]
[L] X [L] X [L]
= [M]
[L3]
= [ML-3]
Hence the dimensions of density are 1 in mass and − 3 in length.

35. USES OF DIMENSION
• To check the correctness of equation
• To convert units
• To derive a formula
To check the correctness of equation
Consider the equation of displacement,
∆x= vt+ ½ at2
By writing the dimensions we get,
vi t = velocity × time = length × time = [L]
time
at 2 = acceleration × time2 = length /time2 × time2 = [L]
The dimensions of each term are same, hence the equation is
dimensionally correct

36. TO CONVERT UNITS
• Let us convert newton (SI unit of force) into dyne (CGS unit of force) .
The dimensions of force are = [LMT −2 ]
So, 1 newton = (1 m)(1 kg)(1 s) −2
and, 1 dyne = (1 cm)(1 g)(1 s) −2
Thus, 1 newton /1 dyne = (1 m/ 1 cm )(1 kg /1 g)(1 s/1 s) −2
= (100 cm /1 cm) (1000 g/ 1 g)(1 s/1 s) −2
= 100 × 1000 = 105
Therefore, 1 newton = 105 dyne

37. TO DERIVE A FORMULA
• The time period ‘T’ of
oscillation of a simple
pendulum depends on length
‘l’ and acceleration due to
gravity ‘g’.
Let us assume that,
T ∝ 𝑙 a 𝑔 b or T = K 𝑙 a 𝑔 b
K = constant which is
dimensionless Dimensions of T
= [L0M0T1 ]
Dimensions of 𝑙 = [L1M0T0 ]
Dimensions of g = [L1M0T−2 ]
• Thus, [L 0M0T1] = K [L1M0T0 ] a
[L1M0T −2 ] b
= K[LaM0T0] [LbM0T−2b]
[L0M0T1] = K[La+bM0T−2b ]
a + b = 0 & − 2b = 1
∴ b = − 1/2 & a = 1/2
T = K 𝑙 1/2 𝑔 −1/2
∴ T = K √l/g

38. LEAST COUNT OF INSTRUMENTS
• The smallest value that can be measured by the measuring instrument is called its least
count or resolution

39. LC OF LENGTH MEASURING INSTRUMENTS
Screw Gauge Least count = 0.01 mm

40. LC OF MASS MEASURING INSTRUMENTS
Weighing scale Least count = 1 kg Electronic balance Least count = 1 g

41. LC OF TIME MEASURING INSTRUMENTS
Wrist watch Least count = 1 s Stopwatch Least count = 0.01 s

42. PART 3
•Significant Figures and Error
Analysis
–Accuracy and precision of Measuring
Instruments; Errors in
Significant Figures.

43. ACCURACY OF MEASUREMENT
• It refers to the closeness of a measurement to the true
value of the physical quantity.
• Example:
True value of mass = 25.67 kg
Mass measured by student A = 25.61 kg
Mass measured by student B = 25.65 kg
The measurement made by student B is more
accurate.

44. PRECISION OF MEASUREMENT
• It refers to the limit to which a physical quantity is
measured.
• Example:
Time measured by student A = 3.6 s
Time measured by student B = 3.69 s
Time measured by student C = 3.695 s
The measurement made by student C is most
precise.

45. SIGNIFICANT FIGURES
• The total number of digits (reliable digits + last uncertain digit) which are
directly obtained from a particular measurement are called significant figures.

46. RULES FOR SIGNIFICANT FIGURES
I
All non-zero digits are significant.
Number Significant figures
16 2
35.6 3
6438 4
2
Zeros between non-zero digits are significant.
Number Significant figures
205 3
3008 4
60.005 5

47. RULES FOR COUNTING SIGNIFICANT FIGURES
3
Terminal zeros in a number without decimal are not significant unless specified by a least
count.
Number Significant figures
400 1
3050 3
(20 + 1) s 2
4
Terminal zeros that are also to the right of a decimal point in a number are significant.
Number Significant figures
64.00 4
3.60 3
25.060 5

48. RULES FOR COUNTING SIGNIFICANT FIGURES
5
If the number is less than 1, all zeroes before the first non-zero digit are not significant.
Number Significant figures
0.0064 2
0.0850 3
0.0002050 4
6
During conversion of units use powers of 10 to avoid confusion.
Number Significant figures
2.700 m 4
2.700 x 102 cm 4
2.700 x 10−3 km 4

49. EXACT NUMBERS
• Exact numbers are either defined numbers or the
result of a count.
• They have infinite number of significant figures
because they are reliable.
example:
1 dozen 12 numbers
1 hour 60 min
1 inch 2.54 cm
1 second 1000 millisecond

50. RULES FOR ROUNDING OFF A MEASUREMENT
1
If the digit to be dropped is less than 5, then the preceding
digit is left unchanged.
Number Round off up to 3 digits
64.62 64.6
3.651 3.65
546.3 546

51. 2 RULE FOR ROUNDING OFF
If the digit to be dropped is more than 5, then the preceding
digit is raised by one.
Number Round off up to 3
digits
3.479 3.48
93.46 93.5
683.7 684

52. 3 RULES FOR ROUNDING OFF
If the digit to be dropped is 5 followed by digits other than zero,
then the preceding digit is raised by one.
Number Round off up to
3 digits
62.354 62.4
9.6552 9.66
589.51 590

53. 4 RULES FOR ROUNDING OFF
• If the digit to be dropped is 5 followed by zero or nothing, the
last remaining digit is increased by 1 if it is odd, but left as it is
if even.
Number Round off up to 3 digits
53.350 53.4
9.455 9.46
782.5 782

54. SIGNIFICANT FIGURES IN CALCULATIONS
Addition & subtraction
The final result would round to the same decimal place as the least
precise number.
Example:
13.2 + 34.654 + 59.53 = 107.384 = 107.4
19 – 1.567 - 14.6 = 2.833 = 3
Multiplication & division
The final result would round to the same number of significant digits as
the least accurate number.
Example:
1.5 x 3.67 x 2.986 = 16.4379 = 16
6.579/4.56 = 1.508 = 1.51

55. ERRORS IN MEASUREMENT
Difference between the actual value
of a quantity and the value obtained
by a measurement is called an error
Error = actual value – measured
value

56. TYPES OF ERRORS
Systematic errors
Gross errors
Random errors
1. Systematic errors
• These errors are arise due to flaws in experimental system.
• The system involves observer, measuring instrument and the
environment.
• These errors are eliminated by detecting the source of the
error.

57. TYPES OF SYSTEMATIC ERRORS
• Personal errors
• Instrumental errors
• Environmental errors
a. Personal errors
These errors are arise due to faulty procedures adopted by the person making
measurements
PARALLAX ERROR

58. SYSTEMATIC ERRORS - B. INSTRUMENTAL ERRORS
These errors are arise due to faulty construction
of instruments.

59. SYSTEMATIC ERRORS - C. ENVIRONMENTAL ERRORS
• These errors are caused by external conditions like pressure,
temperature, magnetic field, wind etc.
• Following are the steps that one must follow in order to eliminate
the environmental errors:
a. Try to maintain the temperature and humidity of the
laboratory constant by making some arrangements.
b. Ensure that there should not be any external magnetic or
electric field around the instrument.

60. 2. GROSS ERRORS
• These errors are caused by mistake in using
instruments, recording data and calculating results.
• Example:
• a. A person may read a pressure gauge indicating 1.01
Pa as
1.10 Pa.
• b. By mistake a person make use of an ordinary
electronic scale having poor sensitivity to measure
very low masses.

61. 3. RANDOM ERRORS
•These errors are due to unknown causes and
are sometimes termed as chance errors.
• Due to unknown causes, they cannot be
eliminated.
• They can only be reduced and the error
can be estimated by using some statistical
operations.

62. ERROR ANALYSIS
For example, suppose you measure the oscillation period of a pendulum with a stopwatch five times
Trial no 1 2 3 4 5
Measured value 3.9 3.5 3.6 3.7 3.5

63. MEAN VALUE
• The average of all the five readings gives the most probable value for time period.
ix
n
x 
1
6.364.3
5
5.18
5
5.37.36.35.39.3


x

64. ABSOLUTE ERROR
The magnitude of the difference between mean value and each individual value is called
absolute error
ii xxx 
• The absolute error in each individual reading:
Xi 3.9 3.5 3.6 3.7 3.5
∆Xi 0.3 0.1 0 0.1 0.1

65. MEAN ABSOLUTE ERROR & REPORTING OF RESULT
• ∆X =1/n ∆Xi
• ∆X = 0.3+0.1+0+0.1+0.1
5
= 0.6/5 = 0.12= 0.1
The arithmetic mean of all the
absolute errors is called mean
absolute error
• The most common way adopted by
scientist and engineers to report a result
is:
• Result = best estimate ± error
• It represent a range of values and from
that we expect
a true value fall within.
• Thus, the period of oscillation is likely to
be within
(3.6 ± 0.1) s.

66. RELATIVE ERROR & PERCENTAGE ERROR
• The relative error is defined as the
ratio of the mean absolute error to the
mean value.
• relative error = ∆X / X
• ∆X / X =0.1/3.6 = 0.0277 = 0.028
• The relative error multiplied by 100
is called as percentage error.
• percentage error = relative error x
100
• percentage error = 0.028 x 100
• percentage error = 2.8 %

67. LEAST COUNT ERROR
• The least count error of any
instrument is equal to its
resolution.
• Thus, the length of pen is
likely to be within (4.7 ± 0.1)
cm.
Least count error is the error associated with the resolution of the instrument.

68. COMBINATION OF ERRORS
•In different mathematical operations like
addition, subtraction, multiplication and
division the errors are combined according to
some rules.
•Let ∆A be absolute error in measurement of A
• Let ∆B be absolute error in measurement of B
• Let ∆X be absolute error in measurement of X

69. WHEN X = A ± B

70. WHEN X = A × B OR A / B

71. WHEN X = AN

72. PART IV

73. ESTIMATION
• Estimation is a rough calculation to find an approximate value of something that is
useful for some purpose.
• Example :
• Estimate the number of flats in Dubai city

74. ESTIMATE THE VOLUME OF WATER STORED IN A DAM

75. METHODS OF ESTIMATION

76. ORDER OF MAGNITUDE
• The approximate size of
something expressed in powers of
10 is called order of magnitude

77. APPROXIMATE OF NUMBERS
• To get an
approximate idea of
the number, one may
round the coefficient
to
• 1 if it is less than or
equal to 5 and
• 10 if it is greater than
5.
• Examples:
• Mass of electron = 9.1 x 10−31 kg
≈ 10 x 10−31 kg
≈ 10−30 kg
• Mass of observable universe = 1.59 x 1053
kg
≈ 1 x 1053 kg
≈ 1053 kg

78. CH 1 FUNDAMENTAL FORCES IN NATURE
•The forces which we see in our day to day life
like muscular, friction, forces due to
compression and elongation of springs and
strings, fluid and gas pressure, electric,
magnetic, interatomic and intermolecular
forces are derived forces as their originations
are due to a few fundamental forces in nature.

79. A FEW FUNDAMENTAL FORCES ARE:

80. GRAVITATIONAL FORCE
It is the force of mutual attraction between any two objects
by virtue of their masses. It is a universal force as every
object experiences this force due to every other object in the
universe.

82. ELECTROMAGNETIC FORCE
It is the force between
charged particles. Charges
at rest have electric
attraction (between unlike
charges) and repulsion
(between like charges).
Charges in motion produce
magnetic force. Together
they are called
Electromagnetic Force.

84. STRONG NUCLEAR FORCE
• It is the attractive force between
protons and neutrons in a
nucleus.It is charge-
independent and acts equally
between a proton and a proton,
a neutron and a neutron, and a
proton and a neutron. Recent
discoveries show that protons
and neutrons are built of
elementary particles, quarks.

86. WEAK NUCLEAR FORCE
• This force appears only in
certain nuclear processes
such as the β-decay of a
nucleus. In β-decay, the
nucleus emits an electron
and an uncharged particle
called neutrino.This particle
was first predicted by
Wolfgang Pauli in 1931.

88. FUNDAMENTAL FORCES OF NATURE

90. PART V 30/07/2020

91. CH 2 NUMERALS
1. Explain this statement clearly it correct or wrong:
(a) Atoms are very small objects.
(b) a jet plane moves with great speed
(c) the mass of Jupiter is very large
(d) the air inside this room contains a large number of
molecules.
(e) a proton is much more massive than an electron.
(f) the speed of sound is much smaller than the speed
of

92. ANSWER
• (a) The size of an atom is much smaller thanthe sharp tip of a
pin.
• (b) A jet plane moves with a much larger speed than a
superfast train.
• (c) The mass of Jupiter is very large as compared to that
earth.
• (d) The air inside this room contains a very large number
molecules as compared to that in a balloon.
• (e) The given statement is correct
• (f) The given statement is correct.

93. 2.LET US CONSIDER AN EQUATION
•Answer:
• The dimensions of LHS are [M] [LT-1]2 = [M] [L2 T-2]
= [M L2 T-2]
The dimensions of RHS are [M] [LT-2] [L] = [M] [L2T-2]
= [ML2T-2]
The dimensions of LHS and RHS are the same and
hence the equation is dimensionally correct.
1/2 mv2 = mgh

94. • Answer:
The number of significant figures in the measured length is 4. The calculted area and
the volume should therefore be rounded off to 4 significat figures.
Surface area of the cube = 6(7.203)2 m2
= 311.299254 m2
= 311.3 m2
Volume of the cube = (7.203)3 m3
= 373.714754 m3
= 373.7 m3
3. Each side of a circle is measured to be 7.203 m. What are
the total surface area and the volume of the cube to
appropriate significant figures?

95. • Answer :
• There are three significant figures in the measured mass
whereas there are only 3 significant figures in the measured
volume. Hence the density should be expressed to only 2
significant figures.
–Density = 5.74 gcm-3
1.2
= 4.8 gcm-3
4) 5.74 g of a substance occupies 1.2 cm3.
Express its density by keeping the significant figures
in view.