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Physical Quantities and Measurement - Physics For Class IX (Science Group) - Long Questions Answers

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Physics For Class IX (Science Group)
UNIT 1: Physical Quantities and Measurement
Long Questions Answers

Q.1: List with brief description of various branches of physics?
Ans: BRANCHES OF PHYSICS
The branches of Physics are classified on the basis of different areas of study with different approaches.
These branches show the spectrum and scope of Physics around us and help scientist to describe ideas in a well-organized way.
The main branches of Physics are as follows.

1. Mechanics:
This branch of physics is mainly concerned with the laws of motion and gravitation.

2. Thermodynamics:
Thermodynamics deals with heat and temperature and their relation to energy and work.

3. Electricity:
Electricity is the study of properties of charges in rest and motion.

4. Magnetism:
Magnetism is the study of magnetic properties of materials.

5. Atomic Physics:
Atomic physics deals with the composition structure and properties of the atom.

6. Optics:
Optics studies physical aspects of light and its properties with the help of optical instruments.

7. Sound:
Sound is the study of production, properties and applications of sound waves.

8. Nuclear physics:
Nuclear physics deals with the constituents, structure, behavior and interactions of atomic nuclei.

9. Particle physics:
Particle Physics studies the elementary constituents of matter and radiation, and the interactions between them.

10. Astrophysics:
The study of celestial objects with the help of laws of physics is known as Astrophysics.

11. Plasma physics:
The study of ionized state of mater and its properties is known as Plasma Physics.

12. Geo physics:
The study of internal structure of earth is known as Geo physics.

Q.2: Define measurement and physical quantities? Describe types of physical quantities?
Ans: MEASUREMENT:
It is the determination of the size or magnitude of something. It is explained with the help of describing the mathematical relations between various physical quantities.

PHYSICAL QUANTITIES
The notion of physical dimension of a physical quantity was introduced by Joseph Fourier in 1822 by convention. All physical quantities are important for describing the nature around us. All physical quantities are either calculated mathematically or measured through an instrument. A physical quantity has magnitude and unit. It can be define as:

DEFINITION:
A physical quantity is a physical property of a phenomenon, body, or substance that can be quantified by measurement.

OR

A physical quantity can be expressed as the combination of a magnitude expressed by a number – usually a real number – and a unit.

TYPES OF PHYSICAL QUANTITIES QUANTITIES:
Physical quantities are classified into two categories:

1. Fundamental Or Base Physical Quantities
2. Derived Physical Quantities.

FUNDAMENTAL OR BASE PHYSICAL QUANTITIES:
Physical quantities which cannot be explained by other physical quantities are called fundamental physical quantities.
There are seven fundamental physical quantities with their units, which are:

Fundamental Or Base quantities and their S.I units:

Fundamental quantities	Symbol of quantity	S.I Unit	Symbol of Unit
Length	l	meter	m
Mass	M	Kilogram	kg
Time	t	second	s
Electric current	I	Ampere	A
Temperature	T	Kelvin	K
Amount of substance	Iv	mole	mol
Luminous intensity	n	candela	cd

DERIVED PHYSICAL QUANTITIES:
Physical quantities which are explained on the basis of fundamental physical quantities are called derived physical quantities.
Following are some derived quantities and their units:

Derived Quantities and their S.I units:

Derived Quantities	Symbol of quantity	S.I Unit	Symbol of Unit
Volume	V	cubic meter	m3
Velocity	v	meter per second	m-1s
Force	F	Newton	N
Density	D	kilogram per cubic meter	kg/m3
Acceleration	a	meter per second square	m/s2
Power	P	Pascal	Pa {N/m2 or Nm-2}
Work	W	Joule	J {Nm}
Charge	Q	Columb	C

UNITLESS PHYSICAL QUANTITIES:
Some Physical quantities are unitless, i.e. they do not have any unit.
Example: Such as Elastic modulus, Plane angle and solid angle

Q.3: Define length and the standard of length or S.I unit of length? Also write down the multiples and sub multiples of S.I unit of length?
Ans: LENGTH:
If there is any measurement that has proven to be the most useful to humanity, it is length.
For examples units of length include the inch, foot, yard, mile, meter etc.
Definition:
"The length is defined as the minimum distance between two points lying on same plane."

THE STANDARD OF LENGTH OR S.I. UNIT OF LENGTH - METER:
The standard of length is meter. OR The meter (m) is the SI unit of length and is defined as:
The length of the path traveled by light in vacuum during the time interval of 1/299 792 458 of a second.

OR

Meter is also define as the distance between two marks engraved on an iridium - platinum alloy bar kept at 0℃ in the international bureau of weights and measures near Paris.
1 meter = 1650763.73 wavelengths of krypton (Kr) atom in a vacuum.

INSTRUMENT USE TO MEASURE LENGTH:
The basic measurement of length can be obtained with the help of a measuring tape , or meter rule or meter rod or an inch tape.

MULTIPLE AND SUB MULTIPLES OF SI UNIT OF LENGTH:
The multiples and sub-multiples units of a meter are very easily obtained by multiplying and dividing it by 10 as follow:

(kilometer = km, meter = m,  centimeter = cm,  millimeter = mm,  micrometer = µm,  nanometer = nm)

• 1 inch = 2.53 cm
• 12 inch = 1 ft
• 1 yard = 3 ft

Q.5: What is meter rule? Describe construction and working of meter rule? OR What is meter rule? How can we use a meter rule to measure length?
Ans: METER RULE:
A meter rule is a device which is used to measure length of different objects.

CONSTRUCTION:

• A meter rule of length 1 m is equal to 100 centimeters (cm).
• On meter rule each cm is divided further in to 10 divisions which are called millimeters (mm). So, a meter rule can measure up to 1 mm as smallest reading.
• It is made up of a long rigid piece of wood or steel.

WORKING:
The zero-end of the meter rule is first aligned with one end of the object and the reading is taken where the other end of the object meets the meter rule.

Q.6: What is vernier calipers? What are its major parts? OR Write down the construction of Vernier calipers? How can we take reading from vernier caliper or How can we raed it? Give example also?
Ans: VERNIER CALIPER:
The Vernier Caliper is a precision instrument that can be used to measure internal and external distance extremely accurate.

CONSTRUCTION:
The Vernier Caliper is a meter stick graduated in millimeters used to measure a distance up to 1 mm. It has both an imperial (measure in inches) and metric (measure in millimeter) scale.

Parts Of Vernier Caliper:

1. Vernier Calipers consists of
2. A pair of calipers having a Main Scale and Vernier Scale.
3. Jaws.
4. Thin Flat Rod Or Depth Gauge.

Main Scale (MS):

• A vernier scale consists of a rectangular steel bar whose one side (smaller lines) is graduated in millimeters and the longer lines on the main scale represent centimeter.
• Each division on the main scale is 1 mm (0.1 cm).
• The main scale is fixed in place.
• Its left upper part has a fixed jaw.

Vernier Scale (VS):

• Vernier scale is the name for the sliding scale that opens and closes the jaws.
• It usually consisting of 10 division and slides over the main scale.
• The left upper part of this scale has a moveable jaw.

Jaws:

• A Vernier caliper has two main jaws that are used for measuring external diameter, as well as smaller jaws that are used for measuring the internal diameter of objects.
• These jaws are also called calipers
• Each jaws has two jaw "Fixed" and "Movable".
• Fixed jaw lies on the rectangular bar while jaw moveable jaw is slides over the main scale and is provided with a vernier scale.
• When both jaws touch each other, the zero of the vernier scale coincides with zero of the main scale. Its mean there is no zero error.

Thin Flat Rod OR Depth Gauge:

• A thin flat rod is attached to the sliding scale on its back which can measure the internal depth of a hallow cylinder.

READING OF VERNIER CALIPERS:
The diameter of a small sphere object can be measured with the help of this device.

Zero Error:
Before the measurement, close the jaws of the vernier calipers completely and note down whether the zero line of the vernier scale coincides with the zero of the main scale.

• If they coincide, there is no zero error. (No zero error, No correction required)
• If zero mark on vernier scale is slightly to the right, zero error is positive. (The positive zero error is subtracted from reading)
• If  zero mark on vernier scale is slightly to the left, zero error is negative. (Negative zero error is added to the reading)

Observed Reading

• Step 1:
  Place the object between the jaws of the Vernier caliper, so that the cylinder is held tightly between jaws.
  
  
• Step 2:
  Note the main scale reading by counting lines before the zero line of Vernier scale.
  
  
• Step 3:
  Count the next line of Vernier scale after zero coinciding main scale.
  
  
• Step 4:
  Add the two reading for total (Main Scale Reading + Vernier Scale Reading = Total Reading)
  
  

EXAMPLE:

Q.7: What is Micrometer Screw Gauge? What are its major parts? OR Write down the construction of Micrometer Screw Gauge? How can we take reading from Micrometer Screw Gauge Or How can we read it? Give example also?
Ans: MICROMETER SCREW GAUGE:
Screw gauge in extensively used in engineering field for obtaining precision measurements.
Micrometer screw gauge is used for measuring extremely small dimensions or very small lengths such as the diameter of a wire or sphere so as to get readings accurate up to 3^rd or 4^th place of decimal. It can measure accurately up to one hundredth part of a millimetre.

OR

A screw gauge can even measure dimensions smaller than those measured by a Vernier Caliper. It is an instrument that can measure small length or thickness correctly up to ¹ / ₁₀₀₀ of millimetre or up to three place of decimals.

Construction:

• Major Parts:- It consists of:
• U - shaped metallic frame
• Fixed stud
• Movable stud
• Main scale with datum (reference) line
• Thimble (Circular) scale
• Drum
• Ratchet

U - shaped metallic frame having a fixed stud at one end, while a screw passes through the other end and has a hallow cylinder. A millimetre scale is graduated on the fixed nut of the hallow cylinder along a datum line which is parallel to its axis. This scale is known as Main scale.
The hallow cylinder act as a nut. The screw has a movable end. A cap called ratchet is provided at the end of the screw and it can be rotated to move the screw forward or backward. The left end of this cap has a Thimble scale which is usually divided into 100 or 50 equal divisions.

Reading A Micrometer Screw Gauge
Micrometer Screw gauge works on the simple principle of converting small distances into larger ones by measuring the rotation of the screw. This “screw" principle facilitates reading of smaller distances on a scale after amplifying them.

Zero Error:
Bring the spindle and the anvil together without applying undue pressure.

• If Zero mark on thimble scale (circular scale) coincides with the datum line (reference line) on the main scale and reading on the main scale is zero. No zero error. (No zero error, No Correction is required)
• If zero on datum line can be seen (i.e zero lies below datum line). Positive Zero Error. (The positive zero error is subtracted from reading)
• If zero mark on datum line cannot be seen(i.e zero lies above datum line). Negative zero error. (Negative zero error is added to the reading)

Observed Reading:

• Step 1:
  Turn the thimble until the anvil and the spindle gently grip the object. Then turn the ratchet until it starts to click.
  
  
• Step 2:
  Take the main scale reading at the edge of the thimble.
  
  
• Step 3:
  Take the thimble scale reading opposite the datum line of the main scale. Multiply this reading with least count i.e., 0.01 mm.
  
  
• Step 4:
  Now add main scale reading to thimble reading. This will be the diameter of the object.
  
  

EXAMPLE:

Q.8: Define standard of mass or S.I unit of mass? Also write down the multiples and sub multiples of S.I unit of mass?
Ans: THE STANDARD OF MASS OR S.I. UNIT OF MASS - KILOGRAM:
The kilogram is the SI unit of mass and is equal to the mass of the international prototype of the kilogram, a platinum-iridium standard that is kept at the International Bureau of Weights and Measures.

OR

The kilogram, originally defined as:
The mass of one cubic decimeter of water at the temperature of maximum density. It was replaced after the International Metric Convention in 1875 by the International Prototype Kilogram.

OR

The kilogram is a cylinder of special metal about 39 millimeters wide by 39 millimeters tall that serves as the world's mass standard.

National Prototype Meter and Kilogram:
Each country that subscribed to the International Metric Convention was assigned one or more copies of the international standards; these are known as National Prototype Meter and Kilogram.

INSTRUMENT USE TO MEASURE MASS:
The Physical balance is an instrument used for measurement of mass.

MULTIPLE AND SUB MULTIPLES OF SI UNIT OF MASS:
Few of its Multiples and sub multiples are given below:

• 1g = 1000000 mg = 10⁶ mg
• 1g = 1000000000 ng = 10 ⁹ ng
• 1g = 0.002lb

Q.9: Define standard of time or S.I unit of time? Also write down the multiples and sub multiples of S.I unit of time?
Ans: THE STANDARD OF TIME OR S.I. UNIT OF TIME - SECOND:
Before 1960, the standard of time (second) was defined in terms of ¹ / _86,400th part of the mean solar day for the year 1900. The rotation of the Earth is now known to vary slightly with time, this motion is not a good one to use for defining a time standard.

Since 1967 till now, the second was redefined to take advantage of the high precision attainable in a device known as an atomic clock, which uses the characteristic frequency of the cesium-133 atom as the “reference clock”. One such clock is at National Bureau of Standards, Washington, U.S.A.

DEFINITION OF SECOND:
A second is defined in terms of a time period of vibration of radiation from the Cesium atom of mass number 133 (Cs-133). one second is 9,192,631,770 period of vibration of Cs-133 This unit of time is ascertained through Cesium atomic clock.

INSTRUMENT USE TO MEASURE TIME:
A stopwatch is used to measure the time interval between two events. For more accurate measurement of time intervals light gates can be used.

MULTIPLE AND SUB MULTIPLES OF SECOND:
Its related Multiples and sub multiples are given below:

• 1 hour = 60 min
• 1 hour = 3600 sec
• 1 min = 60 sec
• 1 sec = 1000 ms = 10³ ms
• 1 sec = 1000000 μs = 10⁶ μs
• 1 sec = 1000000000 ns = 10⁹ ns
• 1 sec = ¹ / ₆₀ hr.
• 1 sec = ¹ / ₆₀ min
• 1 sec = ¹ / ₃₆₆₀ hr. (hour)
• 1 ms (millisecond) = ¹ / ₁₀₀₀ s = 1000^-3 s
• 1 µs (microsecond) = ¹ / _{1,000 000} s = 10^-6 s
• 1 ns (nanosecond) = ¹ / _{1,000 000 000} s = 10^-9s

(Note: hr. (Hour), min (Minute), sec or s (Second), ms (Millisecond), μs (Microsecond), ns (nanosecond)

Q.10: What is stop watch? describe its types?
Ans: STOP WATCH:
A stopwatch is used to measure the time interval between two events.

Types Of Stop Watch:
There are two types of stopwatch:

1. Mechanical stopwatch and
2. Digital stopwatch

Mechanical / Analogue Stopwatch:

• A mechanical stop watch can measure a time interval up to 0.1 second.
• It has a knob that used to wind the spring that powers the watch.
• It can also be used as a start stop and reset button.
• The watch starts when the knob is pressed once. When pressed second time, the watch stops. While the third press brings the needle back to zero.

Digital Stopwatch:

• A digital stop watch can measure a time interval up to 0.01 second.
• It starts to indicate the time lapsed as the start/stop button is pressed.
• As soon as start/stop button is pressed again, it stops and indicates the time interval recorded by it between start and stop of an event.
• A reset button restores its initial zero setting.
• Now a days almost the mobile phones have a stopwatch function.

Q.11: What is prefixes? Give multiples and fractions of S.I. prefixes?
Ans: PREFIXES:
The Physical quantities are described by the scientist in terms of magnitudes and units. A unit prefix is a specifier. It indicates multiples or fractions of the units.
Use:
Units play a vital role in expressing a quantity either base or derived. Prefixes are useful for expressing units of physical quantities that are either very big or very small.

Representation Of Prefixes In Metric System:
Unit of various sizes are commonly formed by such prefixes. The prefixes of the metric system, such as kilo and milli , represent multiplication by powers of ten.
Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognized by standards organizations.

Prefixes And Their Symbols To Indicate Multiple And Sub-multiple For Both Base And Derived Units

Q.12: .What is scientific notation? Give examples also?
Ans: SCIENTIFIC NOTATION:
Scientific notation or the standard form is a simple method of writing very large numbers or very small numbers. In this method numbers are written as powers of ten. Thus calculation of very large or very small numbers becomes easy.

Parts Of Scientific Notation:
Numbers in Scientific Notation are made up of three parts:

1. The coefficient:
   The coefficient must be equal to or (Not zero) greater than one.
   
   
2. The base:
   The base must be 10.
   
   
3. The exponent.
   The exponent can be negative or positive.
   

Formula:
In scientific notation the numerical part of a measurement is expressed as the product of a number between 1 and 10 and whole number power of ten.

M x 10ⁿ

Where,
M = coefficient
10 = Base
n = Exponent
In this expression 1 ≤ M < 10 and n is an integer.

Example 1:
Mass Of Sun is 2 000 000 000 000 000 000 000 000 000 000 kg.

• In this value decimal lies at the end.
• Move the decimal to left writing in terms of base of ten.
• Power of exponent is taken as positive because value is greater than 1 and we move decimal from left to right.

In scientific notation mass of Sun = M_sun = 2.00 x 10³⁰kg.

Example 2:
Mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 911 kg.

• In this value decimal lies on the left side of the value.
• Move the decimal to right writing in terms of base of ten.
• Power of exponent is taken as negative because value is less than 1 and we move decimal from right to left.

In scientific notation Mass of an electron = M_electron = 9.11 x 10^-31 kg.

Q.13: How can we find the volume of different substances?
Ans: MEASURING THE VOLUME OF DIFFERENT SUBSTANCES:
For density to be measured or calculated we first need to find the volume of substances. Most of solid geometrical shapes have formulae for their volume which is obtained through different parameters such as radius, height, depth, width, base and length, but for irregular objects, liquids and gases this approach is unusual.

1. VOLUME OF LIQUID:

• The volume of liquids can be measured with the help of Cylinders, and Beakers.
• A volume of about a liter or so can be measured using a measuring cylinder.
• When the liquid is poured into the cylinder the level on scale gives the volume.
• Most measuring cylinders have scales marked in milliliters (ml) or cubic centimeters (cm³).
• It should be noted that while recording the value from cylinder the eyes should maintain the level with the value.
• Angular observation may result a false reading of the volume.

2. VOLUME OF REGULAR SOLID:

• If an object has a regular shape its volume can be calculated
• For instance:
  i) Volume of a rectangular block = length x width x height
  ii) Volume of a cylinder = π x radius² x height

3. VOLUME OF IRREGULAR SOLID:

• For an irregular solid its volume is calculated by lowering the object in a partially filled measuring cylinder.
• The rise in the level on the volume scale gives the volume of that object.
• Thus the volume of irregular solid is calculated by subtracting the original volume of liquid from the raised volume of liquid. The total volume is found.
  i.e. Total Volume Of Irregular Solid = Original volume of liquid - Raised volume of liquid.

Experiment:

• The volume of the solid is measured in a separate experiment and then subtracted from the total volume.
• Take a measuring cylinder of 1 liter capacity at full place it in a beaker.
• Fill cylinder full with water.
• Pour a stone of irregular shape in it gradually.
• As we pour the stone in the cylinder, the water from cylinder drops into the beaker.
• Drop the stone in cylinder completely.
• Calculate the volume of water ejected out of cylinder.
• Volume of water ejected is the volume of the stone.

Q.14:Define term density with S.I unit and also define relative density (specific gravity)?
Ans: DENSITY:
The term density of a substance is defined as mass of substance (m) per unit volume (V). It is denoted by Greek letter ρ (rho).

ρ = m / v

Density is characteristic property of any pure substance.
Objects made of a particular pure substance such as pure Gold can have any size or mass but its density will be same for each. In accordance with the above equation mass of a substance can be expressed as

m = ρV

S.I Unit Of Density:
The S.I unit for density is kg/m³ or kgm^-3. Sometimes density of substances is given in gm/ cm³.

Example:
The density of Aluminum is 2.70 gm/cm³ which is equal to 2700 Kg/m³.

RELATIVE DENSITY OR SPECIFIC GRAVITY (Measuring the Density):
There are two ways of finding the density of a substance either mathematically or experimentally by taking density of water at 4°C as a reference which is sometimes known as relative density or 'Specific gravity'.

Unit Of Relative Density:
It has no unit because its a ratio of two substances. It is a number whose value is the same as that of the density in g/cm³.

Formula:

Relative Density = Density of substance / Density of water at 4°C.

Q.15: Define significant figures? Write down rules for determining significant figures?
Ans: SIGNIFICANT FIGURES:
Engineers and scientist around the world work with numbers either representing a large or small magnitude of a physical quantity. The engineers are however interested in the accuracy of a value as they mostly work on estimation but scientist especially physicist are more concerned in the accuracy of these numbers.
For instance, an engineer records the speed of wind and explains it on an average. On the other hand, for the physicist, the speed of earth on its course, the speed of light in vacuum the mass or charge on an electron is just not a matter of numbers but accurate numbers.
Definition:

"The numbers of reliably known digits in a value are known as significant figures."

Rules for determining significant figures:

• Rule 1. All non-zeroes are significant.
  Example: 2.25 (3 significant figures)
  
  
• Rule 2. Leading zeroes are NOT significant.
  Example: 0.00000034 (2 significant figures)
  
  
• Rule 3. Trailing zeroes are significant ONLY if an explicit decimal point is present.
  Example:
  200 (1 significant figure)
  200. (3 significant figures)
  2.00 (3 significant figures)
  
  
• Rule 4. Trapped zeroes are significant.
  Example:
  0.00509 (3 significant figures)
  2045 (4 significant figures)

Physical Quantities and Measurement - Physics For Class IX (Science Group) - Short Questions Answers And Self Assessment Questions

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Physics For Class IX (Science Group)
UNIT 1: Physical Quantities and Measurement
Short Questions Answers

Q.1: Define nature and science?
Ans: NATURE:
Nature is described as a pragmatic set of rules followed by all the things around us. It is something which is much greater than the imagination of humans. It is observable, it is surprising but it is somehow explainable, its architecture has been designed with very beautiful patterns, strict rules but with simplicity. A science which explores the nature is Physics

SCIENCE:
The word science refers to the study of a fact by collecting information through observation, presenting it in a mathematical way, justifying the idea with experiment and finally making a conclusion about the fact.

Q.2: Define Physics?
Ans: PHYSICS:
One of the most basic and ancient science is the Physics. Physics Derived from Ancient Greek ‘physicos’ meaning ‘knowledge of nature’.
Thus physics can be defined as:
Physics is the branch of science which deals with studies of matter its composition, properties, and interaction with energy.

OR

It basically deals with the behavior and structure of matter and the energy that derives the matter.

OR

Physics is the branch of natural science that studies matter, its motion, its behavior through space and time and the related entities of energy and force.

OR

Physics is the branch of science which observes the nature represents it mathematically and conclude with the experiment

Q.3: Why do we study physics?

• Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.
• It is a matter of fact that Physics can be considered as the mother of all sciences.
• The beauty of physics lies in its Laws that govern this whole universe from an atom to large scale galaxies and in its experiments from home to large scale experiment labs.

Q. 4: How many categories or types of Physiiscist are there? Define each.
Ans: TYPES OF PHYSICIST:
Physicist are categorized into two categories:

1. Theoretical physicist
2. Experimental physicists

THEORETICAL PHYSICIST:
Those who observe the nature solve its mysteries with available and missing information, present their theories with mathematical approach. They are known as theoretical physicist.

EXPERIMENTAL PHYSICIST:
Those who are more interested to test those theories with experiments are known as experimental physicists.

Q.5: Describe the crucial role of Physics in Science, Technology and Society? OR What is the importance of physics?
Ans: Importance of Physics in Science Technology and Society

• Society’s reliance on technology represents the importance of physics in daily life.
• Many aspects of modern society would not have been possible without the important scientific discoveries made in the past. These discoveries became the foundation on which current technologies were developed.
• Discoveries such as magnetism, electricity, conductors and others made modern conveniences, such as television, computers, smart phones, medical instruments, other business and home technologies possible.
• Moreover, modern means of transportation, such as aircraft and telecommunications, have drawn people across the world closer together all rely on concepts of physics.

Q.6: What do you know about scientific are physical instruments?
Ans: All physical quantities are either calculated mathematically or measured through an instrument. Scientist, Engineers, Doctors and others like blacksmith, carpenter, and goldsmith even the workers and ordinary human's measure those physical quantities with the help of instruments.
For instance,

• Doctor uses a thermometer to tell our body temperature.
• A carpenter uses the inch tape to measure the length of woods required for furniture.
• A puncture mender uses air gauges to check the air pressure in the tyre.
• Similarly, a chemical engineer uses hydrometer for describing the density of a liquid.
• Measuring the physical quantity correctly with instrument is not an easy task for scientist and engineers. Scientist are seriously concerned with the accuracy of the instrument and its synchronization.
• Moreover, the instrument they design mostly for their own sake of research which readably goes on to commercial market.
• Many of the instruments we use today are inventions of pioneers of science.
• Usually, the basic physical quantities that we use in our daily life are measured with basic and simple instruments.

Q.7: Define least count?
Ans: LEAST COUNT:
Use of every instrument is restricted by smallest measurement that it can perform which is called least count.

Q.8: Give the difference between fundamental unit and derived unit?
Ans: DIFFERENCE BETWEEN FUNDAMENTAL UNIT AND DERIVED UNIT

S.No	Fundamental unit	Derived Unit
1.	The physical quantities discovered from first hand knowledge are called fundamental units.	The unit of those physical quantities which are derived from fundamental physical quantities are called derived units.
2.	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.
3.	Fundamental units cannot be expressed in terms of derived units.	Derived units can be expressed in terms of fundamental units.
4.	Only seven fundamental units exist in Metric System or SI system.	There exist a large number of derived units in Metric System.
5.	Examples of fundamental units are Length (Meter, m), Mass (Kilogram, kg), Time (Second, s), Temperature (Kelvin, K), Amount of substance (Mole, mole), Electric current (Ampere, A), Luminous intensity (Candela, cd)	Examples of few derived units are Velocity (m/s), Acceleration (m/s2), Momentum (kg m/s ), Force (N), Density (kg/m3), Energy (J), Power (W), etc.

Q.9: Define Zero Error ? Write down its types?
Ans: ZERO ERROR:
On closing the two jaws of vernier caliper, if the zero of the main scale does not coincide with the zero of the vernier scale, then the instrument has an error called zero error.
There ere two types of zero error:

1. Positive zero error
2. Negative zero error

1- Positive Zero Error:
If the zero of the vernier scale is on the right side of the zero of the main scale, then the zero error will be positive.
To calculate this zero error, check the vernier scale division (E) which exactly coincide with any main scale division. Then,

Zero error (Z.E) = E X L.C

In case of positive error, it is subtracted from the total reading.

2- Negative Zero Error:
If the zero of the vernier scale is on the left side of the zero of the main scale, then the zero error will be negative.
To calculate this zero error, check the vernier scale division (E) which exactly coincide with any main scale division. Then,

Zero error (Z.E) = (10 - E) X L.C

In case of negative error, it is added to the total reading.

Q.10: What is National Prototype Meter and Kilogram?
Ans: National Prototype Meter and Kilogram:
Each country that subscribed to the International Metric Convention was assigned one or more copies of the international standards; these are known as National Prototype Meter and Kilogram.

Q.11: What is physical balance? Write down its major parts and working? OR What is physical balance? How does it work?
Ans: PHYSICAL BALANCE:
The Physical balance is an instrument used for measurement of mass. It is mostly used in laboratory. It works on the principle of moments.

Parts Of Physical Balance:
It consists of:

• A light and rigid beam of brass
• A metallic pillar
• A wooden base
• Two pans
• A metallic pointer
• An ivory scale
• When the beam is horizontal the pointer remains on zero mark on the ivory scale.
• Plumb line
• Levelling Screw
• Glass box

Working:
The plumb line indicates whether the balance is horizontal. In ideal condition the plumb line is aligned with the end of the knob fixed with the pillar. The whole box has leveling screws at the bottom to set it to horizontal. The device is enclosed in a glass box to avoid wind effects.

Q.12: Describe the working of electronic balance? Or What is an electronic balance?
Ans: ELECTRONIC BALANCE:
The Electronic Balance or the digital mass meter is an electronic instrument configured with integrated circuits and it works on the principal of balancing the forces.
The device is turned on and set to zero then object is placed on the plate.
The reading on the screen gives the mass of object.
The electronic balance is available in different ranges of measurement such as micro gram, milligram and kilogram etc.

Q.13: What is meant by human reaction time?  OR Why we use light gates?
Ans: HUMAN REACTION TIME OR USE OF LIGHT GATES:
As analogue or digital or watch is operated by human manually i.e., they have to be started or stopped by hand. This causes a random error in measurement of time i.e called human reaction time. For most people human reaction time is about 0.3- 0.5 s. Therefore more accurate measurement of time intervals light gates can be used.

Q.14: Why are physicists concerned about the property of matter in term of its mass and space? Or Define matter and describe its types in term of their properties?

Ans: MATTER:
Physicist are concerned with a physical quantity, a property of matter which may help to define the nature of matter in terms of its mass and space.
Definition:
"Matter is anything that has mass and occupies space."

THREE STATES OF MATTER:
The three common phases or states of matter are:

1. Solid
2. Liquid and
3. Gas

1.Solid:
A solid maintains a fixed shape and a fixed size, even if same force is applied it not readily change its volume.
2. Liquid:
A liquid does not maintain a fixed shape it takes on the shape of its container. But, like a solid it is not readily compressible, and its volume can be changed significantly only by a large force.
3. Gas:
A gas has neither a fixed shape nor a fixed volume - it will expand to fill its container.

Q.15: What is Measuring Cylinder? How can we measure the volume of liquid by measuring cylinder?
Ans: MEASURING CYLINDER:
Measuring cylinder is a glass or plastic cylinder with a scale-graduated in cubic centimeters or milliliters (ml)

Uses:
It is used to find the volume of liquids.

Process To Measure Volume Of Liquid By Measuring Cylinder:

• The volume of liquids can be measured with the help of Cylinders, and Beakers.
• A volume of about a liter or so can be measured using a measuring cylinder.
• When a liquid is poured, it rises to a certain height in the cylinder.
• Most measuring cylinders have scales marked in milliliters (ml) or cubic centimeters (cm³).
• The level of liquid in the cylinder is noted and volume of the liquid is obtained.
• In order to read the volume correctly we should keep the eye in level with the bottom of the lower meniscus of the liquid surface.
• Angular observation may result a false reading of the volume.

Q.16: How will you find the volume of small stone?
Ans: The volume of the solid is measured in a experiment and then subtracted from the total volume.
Experiment:

• Take a measuring cylinder of 1 liter capacity at full place it in a beaker.
• Fill cylinder full with water.
• Pour a stone of irregular shape in it gradually.
• As we pour the stone in the cylinder, the water from cylinder drops into the beaker.
• Drop the stone in cylinder completely.
• Calculate the volume of water ejected out of cylinder.
• Volume of water ejected is the volume of the stone.

Q.17: How will you determine the thickness of a piece of wire?
Ans: The thickness of a piece of wire can be determined with the help of screw gauge.

Q.18: Which device will you choose to measure the length of a small cylinder?
Ans: We use Meter rule to measure the length of a small cylinder

Q.19: Choose a proper instrument (meter rule, Vernier calipers, screw gauge, physical balance stop watch, measuring cylinder) for the measurement of length, diameter, mass, time and volume in daily life activities.
Ans

Device	Physical Quantity
Meter rule	Length
Vernier calipers, Screw gauge	Diameter
Physical balance	Mass
Stop watch	Time
Measuring cylinder	Volume

Self Assessment Questions

Q.1: What instrument will you choose to measure height of your friend?
Ans: To measure the height of our friend, we can use a meter rule or inch tape. 
When our height is measured at the doctor's clinic, we usually stand next to a device called a stadiometer.
A stadiometer is a long ruler attached to the wall. It has a sliding horizontal headpiece that's adjusted to rest on top of our head. It's a quick way of accurately measuring our height.

Q.2: Can you describe how many seconds are there in a year?
Ans: There are in:

• 1 year = 365 days
• 1 day = 24 hours
• 1 hour = 60 minutes
• 1 minutes = 60 sec

Therefore
One year would equal 365 times 24 times 60 times 60 seconds
OR
1 year = 365 x 24 x 60 x 60 = 31, 536, 000 seconds

Q.3: Which instrument will you choose to measure your mass?
Ans: We will choose weighing machine to measure our weight. 
The scientific word for weight of an object on a scale is known as "mass".  Therefore here we can use the word "weight" and "mass" interchangeably because both are used in everyday language.
For example: "I weigh 70 kg" or " the car's mass is 1 tonne."
Bathroom scales are used to measure a person's weight. They can be analogue or digital. Bathroom scales usually show units in kilograms or grams.

Q.4: Can you tell if the size of a nucleus is up to 10^-15 m. What prefix shall we use to describe its size?
Ans: femto (f) or femtometer (fm) 

Q.5: How can you identify which gas is denser among the gases?
Ans: If the gas is denser, it has high density. So by calculating the density of different gases at constant volume, we can identify less denser or more denser gases.

Q.6: Can you tell how hot air balloon works?
Ans: In hot air balloon the gas inside the balloon is heated by using a burner. So the hot air inside the balloon becomes less dense than the surrounding cooler air. The less dense hot air has enough lifting power to cause the balloon to float and rise into the air.
In order to get back the hot air balloon down, the pilot opens the flap at the top of the balloon to let the hot air go outside and the cooler air takes its place. Thus the density of the air inside the balloon increases hence it slowly comes down.

Q7: Determine the number of significant figures in 00.6022009 and also write down it in scientific notation
Ans: There are 7 significant figures (i.e. 6022009) in given value.
Scientific Notation = 6.022009 x 10^-1

Reasons

1. Fill a tub with water to certain level and mark.
Put some ice in it and observe the water level carefully as well as floating or sinking. Remove the ice from the tub without being melt and put a balloon in it and then observe. Likewise, put a spoon in that tub and observe. Again put an empty can of coke and observe. Can you tell which of all four has more density? And which has more volume?
Reason:
When we put a spoon in that tub it sinks into water, while rest are float on the surface of water. Thus spoon is much denser than rest object and has more density.
Similarly Balloon occupies more space than ice, spoon or empty can of coke. Thus balloon has more volume than rest objects.

2. Why large weight woods floating on the surface of water and iron needle sinks into the water?
Reason:
Iron is “denser” than wood and have more density that is why iron needle sink into water and large weight woods floating on the surface of water.

3. Why the humans in 'Dead Sea' situated in Jordan does not sink while swimming?
REASON:
The humans in that sea while swimming does not sink! This is because the water of sea is much more salty than normal, which raises the density of water.

4. The large weight woods floating on the surface of water. However, an iron needle sinks into the water.
REASON:
Iron is “denser” than wood and water, where as wood is less dense than water that is why needle sinks into water while the large weight woods floating on the surface of water.

5. Why ice floats while a coin sinks in the water?
REASON:
Solid objects are denser and have more weight than liquids. Although ice is a solid but the water is heavier than ice, it displaces the lighter ice, causing the ice to float to the top.
While the coin have more density than the water, and so the coin sink. So anything with more density than water will sink in water, but other objects that have less density than water will float.

6. Which is more accurate Vernier Caliper or a Screw Gauge and why?
Ans: Screw Gauge is more accurate than Vernier Caliper:
REASON: As compare to Vernier calipers, screw gauge is more accurate and precise because a screw gauge can even measure dimensions smaller (such as the diameter of a wire or sphere) than those measured by a Vernier Caliper. The least count of Vernier calipers is 0.1 mm and for screw gauge it is 0.01 mm. So, a screw gauge can measure accurately up to one hundredth part of a millimeter and more accurate than a Vernier caliper.

Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Solved Exercise 1.1

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Unit 1: Real And Complex Numbers
Exercise 1.1

1. Identify the following numbers as rational and irrational numbers and also write each one in separate column.

2. Convert the following into decimal fraction. Also indicate them as terminating and Non-terminating decimal fractions.

3. Represent the following rational numbers on number line.

OR

4. Can you make a list of all rational number between 1 and 2?
Ans: It is Infinite rational number because the the rational number between two whole numbers are always infinite.

And

(i) ⁵/₄ = 1.25
(ii) ³/₂ = 1.5
(iii) ⁷/₄ = 1.75
(iv) ⁹/₈ = 1.125

5. Give reason, why pi (π) is an irrational number?
Ans:  π = ²²/₇ = 3.14285....
Pi (π) is an irrational number because it has non-terminal and non recurring decimal fraction.

6. Tick (✓) the correct statements.
(i) ⁵/₇ is an example of irrational number. ✓
(ii) π is an irrational number. ✓
(iii) 0.31591... is an example of non-terminating and non-repeating decimal fraction. ✓
(iv) 0.123 is an example of recurring decimal fraction. x
(v) ¹/₃, ²/₃ are lying between 0 and 1. ✓
(vi) ¹ /_{√ 3} is an example of rational number. x

Examples

Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Explanation Of Exercise 1.1

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Unit 1: Real And Complex Numbers
Explanation Of Exercise 1.1

SOME IMPORTANT SETS OF NUMBERS:

Following notations will be used for sets of numbers:

• Set of Natural Numbers: N = {1, 2, 3, . . .}
• Set of Whole Numbers: W = {0, 1, 2, 3, . . .}
• Set of Integers: Z = {0, ±1, ±2, ±3, . . }
• Set of Positive Integers: Z+ = {0, +1, +2, +3, . . }
• Set of Negative Integers: Z¯ = {0, -1, -2, -3, . . }
• Set of Positive Prime Numbers: P = {2, 3, 5, 7, 11, . . . }
• Set of Odd Numbers: O = {±1, ±3, ±5, . . . .}
• Set of Even Numbers: E = {0, ±2, ±4, ±6, . . . .}
• Set of Rational Numbers: Q = {x|x = p/q ; p, q ∈ Z, q ≠ 0}
• Set of Irrational Numbers: Q' = {x|x ≠ p/q ; p, q ∈ Z, q ≠ 0}
• Set of Real Numbers: R = Q U Q'
• Also, R⁺ and R^- will denote the set of all positive and negative real numbers, respectively.

All above sets are contained in the set of real numbers. Hence real numbers are classified as:

CLASSIFICATION OF REAL NUMBERS:

REAL NUMBERS:
The set of real numbers is the union of the set of rational and irrational numbers, i.e.

R = Q U Q'

Also, R⁺ and R^- will denote the set of all positive and negative real numbers, respectively.

RATIONAL NUMBERS:
Rational number is a number that can be written as quotient of two integers (i.e. expressed in the form of fraction ^p/_q) are called rational numbers.
In rational numbers q or denominator is not equal to zero

Q = { x | x ; x = ^p/_q ; p,q ∈ Z and q ≠ 0}

All rational numbers contain terminating and non-terminating decimal fractions.
For example:
⁰/₂ is a rational number but ²/₀ is not a rational number because denominator of rational number is never zero.
Similarly 2, -3 are also rational number because the denominator in each number is 1 i.e.

•  ²/₁ = 2 and
•  ^-3/₁ = -3

NOTE: 
Every natural number and integer is also a rational number.
There are infinite rational numbers between any two numbers.

IRRATIONAL NUMBERS:
Numbers that can not be written as quotient of integers are called irrational numbers.
For Example:

• √ 2 = 1.14142135 ....
• √ 3 = 1.7320508 ....
• π = 3.1415926 ..........
• 0.02002002000200002.......

Irrational numbers contain non-terminating decimal fractions only.

DISTINGUISHING DECIMAL REPRESENTATION OF RATIONAL AND IRRATIONAL NUMBERS

1. Terminating Decimal Fractions:
A decimal fraction in which the decimal part contains only a finite number of digits is called a Terminating Decimal Fraction.
All terminating decimal fractions represent rational numbers.
Example:

• (i) ²⁵⁰¹/₁₀₀ = 25.01
• (ii) ²⁴⁵⁸/₁₀₀₀ = 0.2458
• (iii) ⁵/₂ = 2.5
• (iv) ¹/₂ = 0.5

2. Recurring Or Non Terminating Decimal Fractions:
A non-terminating decimal fraction whose decimal parts contain some digits which are repeated again and again in the same order is called a Recurring Or Non Terminating Decimal Fraction.
All non-terminating decimal fractions represent both rational and irrational numbers.
Example:

• √ 2 = 1.14142135 ....
• √ 3 = 1.7320508 ....
• π = 3.1415926 ..........
• 0.02002002000200002.......

NUMBER LINE

It is a line on which we represent the real number at both sides of zero. The numbers are whole number and also integers.

REPRESENT RATIONAL NUMBER (Terminating And Non-Terminating Recurring Decimal) ON THE NUMBER LINE

In order to locate number with terminating and non-terminating recurring decimal on the number line:
Suppose:
The points associated with the rational number ^a/_b, where a, b are positive integers.

• Step 1: Draw a line show whole parts of the fraction or mixed fraction.
• Step 2: Sub-divide the each unit length (points between two numbers) into b equal parts (i.e according to value of denominator).
• Step 3: Select the a^th of division (i.e. point according to numerator and start counting these on number line.)
• Step 4: The right of the origin represent positive value (i.e. ^a/_b) and the left of the origin at the same distance represents negative value (i.e. - ^a/_b)

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