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Measurement of Area, Volume and Density (Class 11 – Physics)
When Humans look at their childhood pictures, the first thing they realize is how tall or heavy they have become as compared to the early stages of their lives. Noticing the increment in the weight or becoming taller is done through measurement. Measurement is required everywhere in order to specifiRead more
When Humans look at their childhood pictures, the first thing they realize is how tall or heavy they have become as compared to the early stages of their lives. Noticing the increment in the weight or becoming taller is done through measurement. Measurement is required everywhere in order to specifically compare a quantity’s value from its original value. There can be many examples where measurement is required, For example, a thermometer is used to measure the temperature in Celsius of the body, the clocks on the wall are used to measure time in hours, and so on.
Measurement
Calculating the value of one quantity by comparing it with the standard value of the same physical quantity is called Measurement. It can be said that measurement associates the physical quantity with its numeric value.
Normally, objects are measured by placing them next to each other, and it can be explained which one is heavier or taller, etc. Measuring an object gives two results- value and unit of the quantity. For example, The length of the scale is 15 cm long where 15 is the value and the centimeter is the unit used for length.
Metric System
Metric system is the system that came from the decimal system and this system is used to measure basic quantities, metric system paves the way for the conversion of units, that is, the conversion of bigger units into smaller and vice-versa is possible due to the system. The basic quantities that are present are meter, gram, and liters, and they are used to measuring quantities of length, volume/mass, and capacity.
Measurement of Length
According to the metric system, length is calculated in meters. However, it can easily be converted into other forms depending upon the requirement, for instance, if the requirement is to measure the bigger quantity, it should be measured in kilometers, if the requirement is to measure something smaller, it should be in centimeters. Let’s say, the requirement is to measure a certain distance, it should either be in meters or kilometers.
Below is the easier way to explain the conversion,
Measurement of Area
In the standard way, the area of any quantity is measured in meter2, since the area is a two-dimensional quantity that is scalar in nature. It involves lengths going in two different directions known as length and breadth. The area of bigger and smaller quantities can be converted easily using different units, for example, if the area of a small table is to be measured, it is measured in cm2 and if the area of the plot is to be measured, the unit used is meter2.
Below is the easier way to explain the conversion,
Measurement of Volume
The volume of any quantity is three-dimensional in nature, that is, the length if going in three directions, unlike length or area, the volume contains capacity. The standard unit used to measure volume is meter3. The unit is converted into bigger and smaller units like decimeter3 or kilometer3 based on how big or small the quantity is, it is done by simply dividing/ multiplying by tens, hundreds, thousands, and so on.
Below is the easier way to explain the conversion,
Measurement of Density
The density of any object is defined as the mass of that object per unit volume. Density tells how close or far away molecules are packed in a certain volume. The very famous scientist known as Archimedes discovered the concept of the Density of an object. In the metric system, Density is measured in kg/m3 and is represented as D or ρ. Therefore, it can be denoted as,
Sample Problems
Question 1: Convert the following: m3 to mm3, liter to meter3, mile3 to km3.
Solution:
Question 2: What is the difference between the metric system and the imperial system of measurement?
Answer:
Question 3: Calculate the density of an object having a mass of 1200kg and its volume is 10m3.
Solution:
Question 4: There are two large boxes filled with biscuits. The first has 10 biscuits and the second has 20 biscuit packets present in it. The box have the same volume. Explain which box will weigh more?
Answer:
Question 5: A cube is given which has a volume of 1000m3. Calculate the surface area of the cube in cm3.
Solution:
Question 6: The length and the breadth of a cuboid are same, but the height is twice in value. If the volume of the cuboid is 54000m3, find the length, breadth and height of the cuboid in centimeters.
Solution:
Question 7: A cm scale has a limit of 15 points, how long is the scale in meters?
Solution:
See lessLength Measurement (Class 11 – Physics)
Previously, length was measured using units such as the length of a foot, the breadth of a palm, and so on. The ‘Cubit’ was one of the first means of measuring length. It is the length of the arm from the elbow to the tip of the fingers. These units vary from person to person, resulting in non-unifoRead more
Previously, length was measured using units such as the length of a foot, the breadth of a palm, and so on. The ‘Cubit’ was one of the first means of measuring length. It is the length of the arm from the elbow to the tip of the fingers. These units vary from person to person, resulting in non-uniform measures.
How can we know how far the moon is from the earth or how far the moon is from the sun? How did we determine the earth’s diameter? Measuring length isn’t always simple or easy. We’ll try to respond to these queries in the sections below. In addition, we will learn about the many methods for measuring length.
Length
In other terms, it is the largest of the two or the highest of three geometrical form or item dimensions. The width and length of a rectangle, for instance, are its dimensions. Furthermore, under the International System of Quantities, length is a quantity with the dimension distance.
The meter, abbreviated as m, is the basic unit for length in the International System of Units (SI). The length or distance is measured in kilometers (km), meters (m), decimeters (dm), centimeters (cm), and millimeters (mm) in the metric system (mm). It is possible to convert quantities from meters to centimeters, kilometers to meters, centimeters to millimeters, and so on.
Measurement of Length
There were no modes of transportation available in ancient times. People used to travel on foot or by using animals to transport goods. Over time, the term “wheel” was coined. This signified a significant shift in human forms of transportation. Since then, new forms of transportation have been invented and improved regularly. The steam engine was created, and it had a great influence and was instrumental in shaping the world as we know it today.
As a result, transportation has a lengthy history. Did the folks have any idea how far they had to go? To go to any location, one must first determine how far away it is. This aids in deciding whether to walk, take the train, bus, or fly to that location. To determine how far apart two locations are, we must first determine the distance between them. But what exactly does measurement imply? What is the best way to measure a physical quantity? The comparing of an unknown amount to a known amount is known as measurement. A numerical number known as “magnitude” and a “unit” are used to indicate the outcome of the measurement. A ‘unit’ is a pre-determined unit of comparison against which other physical quantities are measured.
The length of the foot, the breadth of the palm, and other such quantities were used to measure the length in the past. The ‘Cubit’ was one of the first means of measuring length. It is the length of an arm measured from elbow to tips of fingers. These units varied from person to person, resulting in non-uniform measures. A set of standard units of measurement has been recognised all around the world to preserve uniformity in measurements.
Conventional Methods of Measurements
Historically, the human body served as the foundation for length units.
A foot is 12 inches long, and a yard is three feet long. It was simple to describe how distant the next village was and to determine if an object would fit through a doorway using these dimensions. These dimensions also made it easier for individuals to swap garments and wood.
Scale
Triangulation Method
Let’s take a closer look at what the triangulation approach entails. How might triangulation assist us in determining the distances between distant stars? The parallax approach makes use of the fact that a triangle may be entirely defined using only three parts. Triangulation is the process of determining the values of a triangle to determine an item’s position. Surveyors and architects frequently employ such techniques.
Triangulation Example
Let’s put this into practice with a real-life scenario. How can we estimate a large object distance from any distance without actually measuring it? It may be measured using the triangulation method.
Triangulation Method of measurement
Parallax Method
The two places of vision each have their own line of sight, and parallax is defined as half the angle between them. When you’re driving in a car and glance about, you’ll notice that items far away appear to move more slowly than items closer to you. This is the parallax effect. Because the parallax of nearby objects is greater than that of distant ones, the parallax may be utilised to measure distances.
When the phenomena of parallax is coupled with triangulation, the position of the item may be determined with great precision. The parallax method is commonly used by astronomers to determine the distances between stars.
Distance Measurement by Parallax Method
The principle of triangulation is used to the measuring of distance through parallax. We learned from triangulation that a triangle may be completely specified if two angles and sides are known.
The distance of a faraway star is being computed in the image below. The star closer to Earth than the farthest one gives the limited parallax value. By observing the star from two known places on Earth that form the triangle’s baseline, we may determine the value of the parallax angle.
Parallax Method
Let’s denote the parallax half-angle between two places on Earth ‘p.’ The radius of the Earth is the greatest value of ‘d,’ and the distance of the star may be considered to be just slightly more than that of the sun. Because the distance from the sun is several orders of magnitude lower than the radius of the Earth, the parallax angle we obtain is exceedingly modest.
Application
The distance to an object measured in parsecs (in terms of light speed) is equal to the reciprocal of parallax angle measured in arcseconds.
Relation between the distance of a star, and its parallax is given as:
To solve the difficulty of tiny ratios, the parallax of a star is most commonly estimated using yearly parallax, which is defined as the difference in a star’s location as seen from the Earth and the Sun. Instead of using the Earth’s radius as a fixed baseline, the radius of the Earth’s revolution around the Sun is used, which increases the size of the baseline and hence the top angle, making it simpler to measure.
However, for any celestial objects near to the Earth, we can consider the diameter of the Earth as a baseline, and the distance of any celestial objects is given as:
Sample Problems
Problem 1: If a person covers 1.5 yards in one step, how much distance will he cover in 30 steps?
Solution:
Problem 2: Astronomers apply which method to determine how far away a star is?
Answer:
Problem 3: What is parallax?
Answer:
Problem 4: What was the conventional method of measuring the length?
Answer:
Problem 5: The Moon subtends an angle of 1° 55’ at the baseline equal to the diameter of the Earth. What is the distance of the Moon from the Earth? (Radius of the Earth is 6.4 × 106 m)
Solution:
See lessSystem of Units (Class 11 – Physics)
Measurement forms the fundamental principle to various other branches of science, that is, construction and engineering services. Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurements find a role in everyday activities to aRead more
Measurement forms the fundamental principle to various other branches of science, that is, construction and engineering services. Measurement is defined as the action of associating numerical with their possible physical quantities and phenomena. Measurements find a role in everyday activities to a large extent. Therefore, it is necessary to study and explore the associated elements along with their theoretical foundations, conditions as well as limitations. It defines the units to be chosen for the measurement of various commodities. It also caters to the comparison of plausible units with the ones already existing of a similar kind.
Measurement defined the new standards as well as form transductions for the quantities which do not have any possible access for direct comparison. These physical quantities can be converted into analogous measurement signals.
Measurements may be made by unaided human senses, generally termed as estimates. It can also be estimated by the use of instruments, which may range in complexity from simple rules for measuring lengths to highly complex analogous systems to handle and design the commodities beyond the capabilities of the senses. Thus, the measurements may range from buying some quantity of milk (in L) or to the highly complex mechanisms, such as radio waves from a distant star or the nuclear bomb radiations. Therefore, we can consider that a measurement, always involves a transfer of energy or interaction between the object and the observer or observing instrument.
Measurement of Height of a person
Unit
The unit of a specified physical quantity can be considered as an arbitrarily chosen standard that can be used to estimate the quantities belonging to similar measurements. The units are well accepted and recognized by the people and well within all guidelines.
The chosen standard is recognized as the unit of that corresponding physical quantity. A standard unit, in short, is a definite amount of a physical quantity. These standard units can be quickly reproduced to create a wide variety of units and are internationally accepted and accessible.
The measurement of any physical quantity is based on a formula, nu,
where, n = numerical value of the measure of the quantity,
u = unit of the quantity.
Standard
The actual physical embodiment of the unit of a physical quantity is termed as a standard of that physical quantity. The standard is expressed in terms of the numerical value (n) and the unit (μ).
Measurement of physical quantity = Numerical value × Unit
For example: Length of a rod = 12 m. Here 12 is its numerical segment and m (meter) is the unit.
Fundamental Units
Fundamental units are elementary in nature, that is, they can be expressed independently without any dependence on any other physical quantity. This implies that it is not possible to resolve it further in terms of any other physical quantity. It is also termed as a basic physical quantity. Fundamental quantities have their own values and units.
Supplementary Fundamental Units
There are two other supplementary fundamental units, namely Radian and steradian are two supplementary which measures plane angle and solid angle respectively.
One radian is equivalent to an angle subtended at the center of a circle by an arc of length equal to the radius of the circle. It is the unit represented for the plane angle.
θ = 1 radian
One steradian is equivalent to the solid angle subtended at the center of a sphere by its surface. Its area is equivalent to the square of the radius of the sphere.It is the unit represented for the solid angle. Solid angle in steradian,
Ω = 1 steradian
Properties of Fundamental Units
Any standard unit should have the following two properties:
The standard unit must be invariable. Thus, defining distance between the tip of the middle finger and the elbow as a unit of length is not invariable.
The standard unit should be easily made available for comparing with other quantities.
The seven fundamental units of S.I. have been defined as under.
Defined as 1650763.73 times the wavelength, in vacuum of the orange light emitted in transition from 2p10 to 5d5.
Defined as the mass of a platinum-iridium cylinder kept at Serves.
Time taken by 9192631770 cycles of the radiation from the hyperfine transition in cesium – 133 when unperturbed by external fields.
The constant current which, if maintained in each of two infinitely long, straight, parallel wires of negligible cross-section placed 1 m apart, in vacuum, produces between the wires a force of 2×10-7 newton per meter length of the wires.
Temperature is measured with absolute zero as the zero and the triple point of water as the upper fixed point on the thermodynamic scale. The interval is divided into 273.15 divisions and each division is considered to be unit temperature.
The luminous intensity in the perpendicular direction of a surface of
The mole is the amount of any substance which contains as many elementary entities as there are atoms in 0.012 kg of the carbon isotope
Derived units
The derived units are in usage for the commodities where the units are obtained from a combination of fundamental units. Derived units are sometimes assigned names. For instance, the S.I unit of force is kg ms-2 , termed as Newton (N). The unit of power is kg m2 s-3 , termed as watt (W).
Steps to find Derived Units
Example: Compute the unit of velocity.
Since, we know velocity is a derived quantity, obtained from distance and time(fundamental quantities).
Mathematically ,
velocity = displacement/time
S.I. unit of velocity =
= m/s
Thus S.I. unit of velocity is m/s.
Some Important derived units
Some of the derived units have been given specific names, depending on the increase in their usage , though they are not recognized in S.I units.
Systems of Units
Any system of units contains the entire set of both fundamental as well as derived units, for all kinds of physical quantities. The preferred system of units are the following :
The unit of length is centimeter, the unit of mass is gram and the unit of time is second according to the guidelines of this system.
The unit of length is foot, the unit of mass is pound and the unit of time is second according to the guidelines of this system.
The unit of length is meter, the unit of mass is kilogram and the unit of time is second according to the guidelines of this system.
The System Internationale d’ Units, that is S.I system contains seven fundamental units and two supplementary fundamental units.
Note:
While computation of values for any physical quantity, the units for the involved derived quantities are treated as algebraic quantities till the desired units are obtained.
Advantages of S.I Unit System
The S.I unit of measurement is preferred over other units of measurement, because,
Other Important Units of Length
The distances can be infinitely larger in magnitude, which cannot be depicted in terms of meters or kilometers. For instance, the distances of planets and stars etc. Therefore, it is necessary to use some larger units of length such as ‘astronomical unit’, ‘light year’, parsec’ etc. while making such calculations, some of which are :
1 AU = 1.496 x 1011 m.
1 light year = 9.46 x 1015 m.
1 parsec = 3.08 x 1016 m
1 fermi = If = 10-15 m
1 angstrom = 1A = 10-10 m
Sample Problems
Problem 1. Convert the unit of G, which is gravitational constant, G = 6.67 x 10-11Nm2/kg2 in CGS system.
Solution:
Problem 2. Name the S.I units of the following commodities :
a. Pressure
b. Solid angle
c. Luminous intensity.
Solution:
Problem 3. Derive the S.I unit of latent heat.
Solution:
Problem 4: How are A0 and A.U related?
Solution:
Problem 5: Describe 1 light-year in meters.
Solution:
See lessDiversity In The Living World (Class 11 – Biology)
Diversity In The Living World Each residing life form will in general share highlights like development, upkeep of homeostasis, propagation, utilization of energy, adaption, and so forth. These highlights help to recognize various species and furthermore prove to be useful in laying out a connectionRead more
Diversity In The Living World
Each residing life form will in general share highlights like development, upkeep of homeostasis, propagation, utilization of energy, adaption, and so forth. These highlights help to recognize various species and furthermore prove to be useful in laying out a connection between organic entities with a typical hereditary part.
Biodiversity: Biodiversity is every one of the various types of life you’ll track down in one region — the range of creatures, plants, growths, and even microorganisms like microbes that make up our normal world. Every one of these animal categories and living beings cooperates in environments, similar to a multifaceted web, to keep up with equilibrium and back life. Biodiversity upholds everything in nature that we want to get by food, clean water, medication, and asylum.
Features of Living World
Diversity in the Living World
The world is overwhelmed by plenty of living organic entities living in the land, water, ice, sweets, and so forth. Each living organic entity is one of a kind of structure, body capabilities, hereditary make-up, etc. The living life forms found in various natural surroundings have different primary organs or capabilities created according to the states of their environment. Organic entities have advanced to adjust to their evolving surroundings. Various sorts and classes of life forms possessing various conditions are known as biodiversity. Districts that are warm and damp have more different organic entities and are called super biodiversity.
People have advanced from primates. However, presently they don’t appear to be comparative in any capacity. Likewise, every individual is not quite the same as the other. Each individual has an alternate skin tone, hair tone, and eyes, and generally significant of everything is hereditary cosmetics. And that implies that the qualities of each and every individual are unique.
In this manner, to recognize better, we have made gatherings of creatures that in some way seem to be comparative and have a few utilitarian and primary similitudes. This is known as order. There are different variables that impact the order of creatures. It is significantly done based on the accompanying models
Classification System
The grouping of life forms is finished by two techniques. One is characterizing them into plants and creatures and the other one which is a five-realm framework is a more nitty-gritty and coordinated characterization of living beings:
Hierarchy of Classification
Carolus Linnaeus additionally organized the organic entities into various scientific classifications at various levels. These scientific classifications in a chronic request are as per the following
Characteristics of Five Kingdoms
Kingdom Monera
These are unicellular prokaryotes. The life forms come up short on the evident nucleus. They might contain a cell wall. They might be heterotrophic or autotrophic in nature. For instance Bacteria, Cyanobacteria.
Kingdom Protista
Protista are unicellular and eukaryotic organic entities go under this group. They display an autotrophic or heterotrophic method of nutrition. They show the presence of pseudopodia, cilia, or flagella for headway. For instance one-celled critter, paramecium.
Kingdom Fungi
These are multicellular, eukaryotic organisms. They have a saprophytic method of nourishment which includes chemoheterotrophic extracellular processing. The cell wall in these organic entities is comprised of chitin. They live in a cooperative relationship with blue-green growth. For instance Yeast, Aspergillus
Kingdom Plantae
These are multicellular, eukaryotic organisms. The cell mass of these creatures is comprised of cellulose. They are heterotrophs and set up their own food through photosynthesis. Kingdom Plantae is partitioned into Thallophyta, Bryophyta, Pteridophyta, Gymnosperms, and Angiosperms. For instance Pines, plants, palm trees, mango trees, and so on.
Kingdom Animalia
Kingdom Animalia is multicellular, eukaryotic living beings yet they don’t show the presence of cell walls. They are heterotrophs or creatures who can’t set up their own food. Both straightforward and complex life forms are found in this gathering and it’s an extremely general gathering of organisms. The organic entities are hereditarily diverse. They display an organ-framework level of organization. It is partitioned into various phyla like Porifera, Coelenterata, Echinodermata, Chordata, Annelids, and so on. For instance Earthworms, Hydra, and so on.
FAQs on Diversity In The Living World
Question 1: Why are living creatures arranged?
Answer:
Question 2: Why are the order frameworks changing occasionally?
Answer:
Question 3: What various measures could you decide to group individuals that you meet frequently?
Answer:
Question 4: What do we gain from distinguishing proof of people and the populace?
Answer:
Question 5: Given underneath is the logical name of Mango. Recognize the accurately composed name. Mangifera Indica
Answer:
Explain Fundamental Forces in Nature (Class 11 – Physics)
Fundamental Forces The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings cRead more
Fundamental Forces
The most beautiful phenomenon that can be seen in physics is that how universe is so disciplined and synced together. The force has kept the universe bind together. Forces have always played an important role in the human existence, but it is not realized by humans. Human beings constantly experience some force acting on them like gravitational force, etc. There are some forces that naturally exist in the universe, they are known as Fundamental Forces. Let’s learn about them in some detail.
Force
Force is an interaction, either with contact or without contact. When there is no opposition given to the Force, It can result in changing the motion, shape, position, of a body. Whenever some interaction occurs between two objects, there is a certain force acting upon them. There are many types of Forces present, For instance, Applied Force, Gravitational Force, Frictional Force, Tension Force, etc.
Fundamental Forces in nature
These forces are so well-defined that they cover the macroscopic and microscopic forces present in nature. The forces learned or seen by humans in everyday life, from frictional force, pull, push, thrust, etc. are known as derived forces, and they are not considered the fundamental forces. The derived forces are actually derived from the fundamental forces in some way or the other. Some Fundamental Forces are,
These above-mentioned forces are responsible for all the observations obtained in forces present in the nature.
Gravitational Force
This force exists by the virtue of the masses of any objects. Gravitational force is the mutual force of attraction between two masses. Attraction between any mass and Earth is called Gravity. Isaac Newton first gave the concept of gravity. Gravity is the most intuitive and the weakest force present in nature. The Irony is that Gravity actually holds the planet, Solar system, Entire Universe together, yet it is known to be the weakest force present in nature.
Electromagnetic Force
Charges when they are at rest exert a force at each other known as the Electric force of attraction/repulsion. Like charges repel each other while unlike charges attract each other. When charges start to move and become dynamic, they develop magnetic field lines around and have magnetic force, these two forces combined are known as Electromagnetic forces present in nature.
Magnetic force produced by current (moving charge)
Combining the above two forces which are always perpendicular to each other will give rise to Electromagnetic Force. The force is produced by massless bosons and photons present in the charges, Electromagnetic force exists in nature and is responsible for many derived forces we experience every day, for example, Friction Force, Normal Force, Elasticity, and so on.
It is the force of attraction between Protons and Neutrons. The force is the same whether protons and protons are present or neutrons and neutrons are present or protons and neutrons are looked at. In short, a Strong nuclear force exists between all nucleons. In short Ranges, this Force is the strongest among all the forces. It is important to note that at a distance of 10-13 cm, this force vanishes.
Weak Nuclear Force
This Force is seen In the β Decay of a nucleus. Scientist named Wolfgang Pauli First predicted a particle named Neutrino. The Neutrino is an uncharged Particle that is released along with the electron in the β Decay process. During β Decay, when Beta Particle is ejected from an Atom, it tends to accelerate away from the atom and some force is required to accelerate the particle known as Weak Nuclear Force. Weak Nuclear Force is stronger than gravitational force but weaker than a strong nuclear force.
Table to represent Range and Relative Strength of Different Forces:
Conceptual Questions
Question 1: Which Fundamental Force is the strongest and weakest among the fundamental forces present in nature?
Answer:
Question 2: Which of the following forces are Fundamental, and which are derived in nature?
Weak Nuclear Force, Friction Force, Gravity, Elasticity, Electromagnetic Force, Push
Answer:
Question 3: A statement is being used now “Gravity is not a force” Throw light on this statement.
Answer:
Question 4: If the masses of 2 objects are doubled and the space between them is also doubled. How will the gravitational Force between them change?
Answer:
Question 5: What are Pseudo Forces? Give Examples.
Answer:
Question 6: Which two forces have infinite range?
Answer:
How is Physics related to Other Sciences?
The word science comes from a Latin verb, Scientia. All the natural phenomena in the universe are governed by a systematic understanding known as Science. Natural phenomena can be predicted, controlled, modified as well as eradicated using the concepts of Science. It can be considered to be a globalRead more
The word science comes from a Latin verb, Scientia. All the natural phenomena in the universe are governed by a systematic understanding known as Science. Natural phenomena can be predicted, controlled, modified as well as eradicated using the concepts of Science. It can be considered to be a global human endeavor. Science is concerned with physical nature and its aspects. It includes imagination, experimentation, and deduction. Knowledge about Science has been gained by humans through experiments, observations, and trials conducted on the surrounding objects. Therefore, it is both knowledge and a process. The systematic and organized knowledge collected through various sources has formed a large pool, which is so vast today that it has been divided into many branches and sub-sections :
Scientific Method and Scientific Theory
The scientific method is a way to gain knowledge in a systematic and organized way. The process in the scientific method involves creating conjectures (hypotheses), deriving predictions out of these, and then carrying out empirical observations to validate those formulated and stipulated conjectures.
The scientific method goes through the formation of a sequence of steps to reach from the knowledge pool to well-formulated derivations and formulae. It consists of the following crucial steps :
Physics and its scope
Physics is the branch of science related to the study of basic laws of nature and their manifestations concerned with the different natural phenomena. It is also referred to as the “fundamental science” because it constrains all the other significant branches of the sciences. It can be considered to be the study of the physical world and matter along with its motion through space and time. It also pertains to the concepts of energy and force as well.
Physics consist of two principal types of approaches :
Scope of Physics
The scope of physics spreads over both massive objects like the universe and its surroundings, as well as to negligibly small-sized particles, like electrons, protons, etc., It is vast as it converts quantities with varying lengths stretching over a magnitude as high as 1060 m (study of the universe) or as low as 10-12 m (study of electrons, protons, etc). It also encompasses a wide range of masses from minutely small, like protons, neutrons etc., 10-10 kg, to highly massive galaxies, 1080 kg. Physics considers both the microscopic and macroscopic domains.
Physics is divided into two major categories based on its scope:
Some Branch of Physics
Physics in Relation to Other Sciences
Physics is a very significant branch of science that plays a crucial role in understanding the developments pertaining to the other branches of science, such as Chemistry, Biology, etc.
The other sciences, like geology, oceanology, seismology, etc, also use some laws of physics.
Sample Problems
Problem 1: What is “high-energy” physics?
Solution:
Problem 2: Explain the relation of physics to seismology.
Solution:
Problem 3: Differentiate between weak and strong nuclear forces.
Solution:
Problem 4: What is the difference between classical and modern physics?
Solution:
Problem 5: Define astrophysics.
Solution:
Problem 6: Explain the reasons behind the durability of scientific knowledge.
Solution:
Problem 7: Is it possible to modify a scientific theory?
Solution:
See lessTypes Of Sets (Class 11 – Maths)
Sets are a well-defined collection of objects. Objects that a set contains are called the elements of the set. We can also consider sets as collections of elements that have a common feature. For example, the collection of even numbers is called the set of even numbers. Table of Content What is Set?Read more
Sets are a well-defined collection of objects. Objects that a set contains are called the elements of the set. We can also consider sets as collections of elements that have a common feature. For example, the collection of even numbers is called the set of even numbers.
Table of Content
What is Set?
A well-defined collection of Objects or items or data is known as a set. The objects or data are known as the element. For Example, the boys in a classroom can be put in one set, all integers from 1 to 100 can become one set, and all prime numbers can be called an Infinite set. The symbol used for sets is {…..}. Only the collection of data with specific characteristics is called a set.
Example: Separate out the collections that can be placed in a set.
Answer:
Types of Sets in Mathematics
Sets are the collection of different elements belonging to the same category and there can be different types of sets seen. A set may have an infinite number of elements, may have no elements at all, may have some elements, may have just one element, and so on. Based on all these different ways, sets are classified into different types.
The different types of sets are:
Singleton Set
Empty Set
Finite Set
Infinite Set
Equal Set
Equivalent Set
Subset
Power Set
Universal Set
Disjoint Sets
Let’s discuss these various types of sets in detail.
Singleton Set
Singleton Sets are those sets that have only 1 element present in them.
Example:
Similarly, all the sets that contain only one element are known as Singleton sets.
Empty Set
Empty sets are also known as Null sets or Void sets. They are the sets with no element/elements in them. They are denoted as ϕ.
Example:
Finite Set
Finite Sets are those which have a finite number of elements present, no matter how much they’re increasing number, as long as they are finite in nature, They will be called a Finite set.
Example:
Infinite Set
Infinite Sets are those that have an infinite number of elements present, cases in which the number of elements is hard to determine are known as infinite sets.
Example:
Equal Set
Two sets having the same elements and an equal number of elements are called equal sets. The elements in the set may be rearranged, or they may be repeated, but they will still be equal sets.
Example:
Equivalent Set
Equivalent Sets are those which have the same number of elements present in them. It is important to note that the elements may be different in both sets but the number of elements present is equal. For Instance, if a set has 6 elements in it, and the other set also has 6 elements present, they are equivalent sets.
Example:
Subset
Set A will be called the Subset of Set B if all the elements present in Set A already belong to Set B. The symbol used for the subset is ⊆
If A is a Subset of B, It will be written as A ⊆ B
Example:
Power Set
Power set of any set A is defined as the set containing all the subsets of set A. It is denoted by the symbol P(A) and read as Power set of A.
For any set A containing n elements, the total number of subsets formed is 2n. Thus, the power set of A, P(A) has 2n elements.
Example: For any set A = {a,b,c}, the power set of A is?
Solution:
Universal Set
A universal set is a set that contains all the elements of the rest of the sets. It can be said that all the sets are the subsets of Universal sets. The universal set is denoted as U.
Example: For Set A = {a, b, c, d} and Set B = {1,2} find the universal set containing both sets.
Solution:
Disjoint Sets
For any two sets A and B which do have no common elements are called Disjoint Sets. The intersection of the Disjoint set is ϕ, now for set A and set B A∩B = ϕ.
Example: Check whether Set A ={a, b, c, d} and Set B= {1,2} are disjoint or not.
Solution:
Also, Check
Summarizing Types of Set
There are different types of sets categorized on various parameters. Some types of sets are mentioned below:
Solved Examples on Types of Sets
Example 1: Represent a universal set on a Venn Diagram.
Solution:
Example 2: Which of the given below sets are equal and which are equivalent in nature?
Solution:
Example 3: Determine the types of the below-given sets,
Solution:
Example 4: Explain which of the following sets are subsets of Set P,
Set P = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
Solution:
FAQs on Types of Sets
What are sets?
What are Sub Sets?
How many types of sets are present?
What is the difference between, ϕ and {ϕ}?
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