Physical World

Which of the following is a key characteristic of a scientific hypothesis?

1. It is a random guess
2. It must be testable and falsifiable (verifiable)
3. It is a proven fact
4. It is the final step in the scientific method

Answer

It must be testable and falsifiable (verifiable)

Reason — A hypothesis is a provisional explanation offered for something that has been observed. What makes it scientific is that it can be put to the test: there must be some possible result that would show it to be wrong. This quality of being testable, and therefore falsifiable, is exactly what marks off a scientific hypothesis from an ordinary guess or opinion.

What is the primary focus of quantum mechanics within the scope of Physics?

1. The study of the motion of planets
2. The behaviour of very large objects
3. The interactions of subatomic particles
4. The study of heat and temperature.

Answer

The interactions of subatomic particles

Reason — Quantum mechanics is the part of physics that deals with how matter behaves at the level of atoms and the particles within them. On this extremely small scale the rules of classical physics no longer hold, and effects such as the fixed energy levels of electrons in an atom can be accounted for only by the quantum description.

What role do the strong and weak nuclear forces play in nature?

1. They govern the behaviour of light
2. They are responsible for gravitational interactions
3. They control the interactions within atomic nuclei
4. They determine the motion of celestial bodies.

Answer

They control the interactions within atomic nuclei

Reason — Both of these forces operate inside the nucleus. The strong force holds the protons and neutrons together, working against the electrical repulsion that would otherwise drive the like-charged protons apart, while the weak force governs certain nuclear changes such as β-decay. Between them they control what goes on within atomic nuclei.

How is the gravitational force unique among the four fundamental forces?

1. It acts only at short distances
2. It affects only charged particles
3. It is always attractive and acts over long distances nuclei
4. It is responsible for the binding of atomic nuclei.

Answer

It is always attractive and acts over long distances

Reason — Of the four fundamental forces, gravitation is the only one that is purely attractive, never repulsive, and it keeps acting even across very great separations. This is why it governs behaviour on the largest scales, such as the orbits of the planets and the binding of stars, whereas the electromagnetic force can both attract and repel.

Note: Option (c) is incorrectly printed as “It is always attractive and acts over long distances nuclei.” The word “nuclei” does not belong in this statement and appears to have been mistakenly copied from option (d). The correct option should read: “It is always attractive and acts over long distances.”

Which of the following statements is true about the nature of physical laws?

1. They are human-made and can change over time
2. They are absolute and unchangeable
3. They are based on extensive experimentation and observation
4. They are only applicable in certain conditions.

Answer

They are based on extensive experimentation and observation

Reason — Physical laws are not framed at will. They are reached by observing nature repeatedly and by checking predictions against experiment, and they are accepted only after surviving such tests. Even so, they stay open to refinement if new evidence should call for it.

What is the significance of Newton's laws of motion in the study of mechanics?

1. They only apply to celestial objects
2. They describe the behaviour of objects in motion and at rest
3. They explain the behaviour of light waves
4. They are applicable only in a vacuum.

Answer

They describe the behaviour of objects in motion and at rest

Reason — Newton's laws of motion are the foundation of classical mechanics. They set out how the forces acting on a body decide its state of motion, and this applies alike to a body kept at rest, one moving uniformly and one that is accelerating. Their usefulness extends from everyday situations right up to the motion of heavenly bodies.

Why is physics considered a fundamental science?

1. It only deals with theoretical concepts
2. It provides the basic principles underlying other sciences
3. It focuses exclusively on mathematical equations
4. It has no practical applications.

Answer

It provides the basic principles underlying other sciences

Reason — Physics is regarded as a fundamental science because the laws it discovers lie beneath the working of the other sciences. Chemistry, biology and the earth sciences all rest in the end on physical principles, so a knowledge of physics supplies the groundwork on which those more specialised subjects are built.

Which of the following technological advancements is a direct result of the study of electromagnetism?

1. Steam engines
2. Satellites
3. Electric generators
4. Nuclear reactors.

Answer

Electric generators

Reason — Electromagnetism deals with the linked behaviour of electric and magnetic fields. The electric generator is a direct outcome of it: by making use of electromagnetic induction, the generator turns mechanical energy into electrical energy, and this is the basis of large-scale power generation.

Which of the following is an example of a physical law?

1. The theory of evolution
2. The law of conservation of energy
3. The concept of natural selection
4. The principle of genetic inheritance.

Answer

The law of conservation of energy

Reason — The law of conservation of energy states that energy is never created or destroyed but only changed from one form into another. Because it holds good everywhere and has been confirmed by experiment time and again, it ranks as a physical law rather than as a mere theory.

Which branch of physics is most concerned with the study of heat and temperature?

1. Optics
2. Thermodynamics
3. Electromagnetism
4. Mechanics.

Answer

Thermodynamics

Reason — Thermodynamics is the branch of physics that treats heat together with work, temperature and energy. The way energy behaves as it is passed on and transformed in different processes is governed by its laws, which is why it is the branch most closely tied to the study of heat and temperature.

Assertion (A): Physics is considered the most fundamental of all sciences.

Reason (R): Physics provides the foundational principles that underlie other sciences like chemistry and biology.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: Physics is concerned with the most basic ingredients of the physical world — matter, energy, space and time — and with the way they act on one another. Since every natural process, however complicated, finally obeys physical laws, physics stands at the base of all the sciences.

Reason (R) is also correct: The other sciences do build upon physical principles; the behaviour of atoms and chemical bonds, or of nerve signals and diffusion in living things, all trace back to physics. It is exactly this that makes physics the most fundamental science, so the reason genuinely accounts for the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): Quantum mechanics is necessary for understanding the behaviour of particles at the atomic and subatomic levels.

Reason (R): Classical physics fails to explain phenomena such as the behaviour of electrons in atoms.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: At the scale of atoms and of the particles inside them, matter does not act in the smooth, predictable manner that classical physics assumes. An electron, for example, shows wave-like and probabilistic behaviour, and only quantum mechanics can describe this properly.

Reason (R) is also correct: Classical physics pictures a particle as having a sharply fixed position and energy, and on that basis it cannot say why the electrons in an atom keep to stable energy levels or why atoms give out sharp spectral lines. Quantum mechanics fills this gap through ideas such as quantised energy and wave functions. Because the classical picture breaks down just where the quantum one succeeds, the reason correctly explains the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): The electromagnetic force is responsible for binding electrons to the nucleus in an atom.

Reason (R): The electromagnetic force acts between charged particles.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: Within an atom the positive nucleus and the negative electrons pull on one another, and it is this pull that keeps the electrons bound about the nucleus. The attraction is electromagnetic, and without it the atom could not stay intact.

Reason (R) is also correct: The electromagnetic force is the force that acts between charged bodies. As the nucleus and the electrons carry opposite charges, this force naturally explains their mutual attraction, so the reason does account for the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): The scientific method involves making observations and conducting experiments.

Reason (R): The scientific method is a systematic approach to understanding natural phenomena.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: To work scientifically is to move through a definite sequence of steps, and noting facts by observation together with putting ideas to the test by experiment are essential parts of that sequence.

Reason (R) is also correct: The scientific method is an ordered routine — observe, propose a hypothesis, test it, and revise the theory where needed — followed in order to make sense of natural events in a consistent way. Since such an ordered routine must include observing and experimenting, the reason explains the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): The weak nuclear force is responsible for radioactive decay.

Reason (R): The weak nuclear force is one of the four fundamental forces in nature.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation

Assertion (A) is correct: Some radioactive changes, and β-emission in particular, are brought about by the weak force. In β-emission a neutron in the nucleus changes into a proton while giving out an electron and an antineutrino, a transformation driven by the weak force.

Reason (R) is also correct: It is quite true that the weak force is one of the four fundamental forces of nature. Yet merely belonging to that group of four tells us nothing about why it should cause radioactive decay, so although both statements are true, the reason does not actually explain the assertion.

Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion (A): The scope of physics includes the study of both macroscopic and microscopic phenomena.

Reason (R): Physics is concerned with understanding the fundamental forces and laws of nature.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: The subject matter of physics reaches across every scale — from large bodies such as planets, vehicles and fluids down to atoms, molecules and subatomic particles — so it takes in both the macroscopic and the microscopic worlds.

Reason (R) is also correct: Physics sets out to uncover the basic laws and forces, such as those of motion, gravitation and electromagnetism, that direct natural phenomena. As these laws hold at every scale, they apply equally to large and to small systems, and the reason therefore explains why the scope of physics covers both.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): The gravitational force between two objects increases as the distance between them decreases.

Reason (R): Gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: Since gravitation grows weaker in step with the square of the separation, bringing two bodies nearer must strengthen the pull between them. So the force does rise as the distance between them shrinks.

Reason (R) is also correct: The gravitational force varies as the product of the two masses and inversely as the square of the distance between them, that is,

$\text F = \text G,\dfrac{\text m_1 \text m_2}{\text r^2}$

It is precisely the r² in the denominator that makes the force increase as the distance falls, so the reason accounts for the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): The law of conservation of energy is a fundamental principle in physics.

Reason (R): Energy can be neither created nor destroyed, only transformed from one form to another.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: The conservation of energy holds in every kind of process — mechanical, thermal, electrical or nuclear — and provides a dependable rule for working out how physical systems behave, which is why it counts as a fundamental principle.

Reason (R) is also correct: The statement that energy is neither created nor destroyed but only converted from one form to another is itself the content of the conservation law: the total energy of an isolated system stays fixed while its form may change. As the reason simply states this principle, it correctly explains the assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): Thermodynamics is the study of heat and its transformation to different forms of energy.

Reason (R): Thermodynamics primarily deals with the principles governing mechanical forces.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: Thermodynamics is concerned with heat and with the way heat is converted into and out of other forms of energy, such as mechanical work. It deals with matters like the flow of heat and the energy changes that go with it.

Reason (R) is incorrect: The study of forces and how they affect motion belongs to mechanics, not to thermodynamics. Thermodynamics is about heat and energy changes rather than about forces, so this statement is wrong.

Therefore, assertion is true but reason is false.

Assertion (A): Newton's laws of motion apply only to objects moving at constant velocities.

Reason (R): Newton's laws describe the relationship between the forces acting on an object and its motion.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are false.

Explanation

Assertion (A) is false: This is not so. Newton's laws cover motion of every sort — a body at rest, one moving uniformly, and one that is accelerating. The second law in fact deals specifically with accelerated motion, so limiting the laws to constant velocity is mistaken.

Reason (R): Newton's laws do state how the forces on a body are tied to its motion — the first law relates force to rest or uniform motion, the second gives the quantitative link between force and acceleration, and the third deals with action-and-reaction pairs. This statement is sound.

Since the assertion is false while the reason is a correct statement, the true combination is "assertion false, reason true", which is not among the four listed options. Of the choices given, option 4 is marked as the answer, on the understanding that the assertion is false.

Note: The given options do not include the case “Assertion is false, but Reason is true.” The Assertion is false because Newton’s laws apply to all objects, whether they are at rest, moving with uniform velocity, or accelerating. The Reason is true because it gives a correct statement. Therefore, the required correct option is missing from the question.

Name two exciting discoveries.

Answer

Two exciting discoveries are :

1. Archimedes' principle, and
2. Earth's gravity.

Name a few 'known' Indian physicists.

Answer

A few well-known Indian physicists are :

• C.V. Raman,
• S. Chandrasekhar,
• S.N. Bose and
• Homi J. Bhabha.

Name a few developments in physics which have a direct impact on daily life.

Answer

Among the developments of physics that bear directly on everyday life are the telephone, the telex, the fax, calculators and computers.

Name the weakest and the strongest forces in nature.

Answer

• Weakest force : Gravitational force
• Strongest force : Nuclear (strong) force

On what scientific basis is the designing of aeroplane wings ?

Answer

The shape of an aeroplane wing is worked out on the basis of Bernoulli's theorem.

Name the phenomenon on which lasers are based.

Answer

The working of a laser rests on the phenomenon of population inversion.

Give an example of mass-energy equivalence.

Answer

A good example is the mutual annihilation of an electron and a positron: the pair disappears and its whole mass reappears as the energy of two gamma-ray photons.

e^- + e⁺ ⟶ γ + γ

Give a brief account of nuclear forces which make them different from other forces.

Answer

Nuclear forces stand apart from the other forces in several ways : they are the strongest forces known, they are non-central and non-conservative, they act only over extremely short ranges, and their strength depends on the spins of the interacting particles.

Explain the relation of physics with chemistry and mathematics.

Answer

Physics and chemistry : Physics hands chemistry its basic ideas. An understanding of atomic structure, of X-ray diffraction and of radioactivity — all of which come from physics — has allowed chemists to arrange the elements in the periodic table, to make sense of valency and chemical bonding, and to work out the structure of complicated molecules.

Physics and mathematics : With mathematics the dependence runs the other way. Physical theories are expressed in mathematical form — electromagnetic theory, for instance, comes down to a set of equations — and mathematics has been an essential tool in building up mechanics, quantum mechanics, electrodynamics and the other theoretical branches of the subject.

Thus, chemistry draws on the principles of physics, while physics in turn depends on mathematics to state and work out its theories.

Give two advancements made in technology on the basis of physics.

Answer

Two such advancements are :

1. The splitting of the nucleus, or nuclear fission, has opened up an enormous supply of energy; in nuclear reactors and in nuclear weapons, energy is released on a large scale as mass is turned into energy.
2. The use of population inversion has given rise to the laser, a device that now finds an extremely wide range of practical uses.

Write in brief the relation of physics with biological sciences.

Answer

Physics is closely bound up with the biological sciences through the instruments and methods it supplies :

• The optical microscope, itself a device of physics, is the biology student's basic tool for examining specimens of leaves and animals.
• Finer structures, such as those inside cells, are studied with the electron microscope.
• X-rays and radio-isotopes are put to use both in detecting and in treating a number of diseases.
• Electronic instruments are used to record the working of the heart and the head.

Explain, with example, the conservation of nucleons.

Answer

The conservation of nucleons means that the total number of nucleons — protons and neutrons taken together — is the same before and after any nuclear reaction. The α-decay of uranium shows this clearly : a uranium nucleus changes into a thorium nucleus with the release of an α-particle, and the nucleon count stays at 238 on both sides of the reaction.

₉₂U²³⁸ ⟶ ₉₀Th²³⁴ + ₂He⁴

Match the scientist's name with the contribution/discovery:

Answer

Match the Indian scientist's name with the contribution/discovery :

Answer

Match the technology with its related scientific principle :

Answer

Physics is the science that tries to make sense of the basic rules by which the universe works, its interest ranging from the smallest subatomic particles to the vast scale of galaxies. Enquiry in physics usually begins with the scientific method — an orderly way of investigating that moves through observing, framing a hypothesis, experimenting and reaching conclusions — and it is by this method that scientists build up theories and models describing the physical world.

The scope of physics is broad, taking in fields such as mechanics, thermodynamics, electromagnetism, quantum mechanics and relativity. Much of its excitement lies in its power to reveal how nature works and to push back the limits of what is known. Its role in technology is just as far-reaching, for physics underlies the advances on which modern life depends; devices from smartphones to medical scanners to the instruments of space exploration all rest on physical principles.

At the heart of the subject lie the basic forces of nature — the gravitational, electromagnetic, strong nuclear and weak nuclear forces — which govern how particles and bodies interact, from the orbits of planets to the binding of nuclei. Beneath these forces stand the physical laws, such as Newton's laws of motion and the laws of thermodynamics, which remain the same everywhere and at all times and give us a means of foretelling how nature will behave.

(i) Which of the following best describes physics?

1. The study of living organisms and their interactions.
2. The exploration of the fundamental principles governing the universe.
3. The examination of chemical reactions.
4. The study of historical events.

(ii) What is the first step in the scientific method?

1. Formulating a hypothesis
2. Conducting an experiment
3. Making an observation
4. Drawing a conclusion.

(iii) Which of the following is not considered a basic force in nature?

1. Gravitational force
2. Electromagnetic force
3. Strong nuclear force
4. Frictional force.

(iv) How does physics contribute to technological advancements?

1. By providing ethical guidelines for technology use
2. By offering explanations for natural phenomena that lead to technological innovations
3. By regulating the production of technological devices
4. By designing software for scientific experiments

(v) Which statement about physical laws is correct?

1. They vary depending on the location in the universe
2. They are hypotheses that are yet to be proven
3. They are universal and consistent across time and space
4. They only apply to certain fields of science.

Answer

(i) The exploration of the fundamental principles governing the universe.

Reason — Physics is marked out by its concern with the basic laws and principles behind natural phenomena, reaching from subatomic particles up to galaxies.

(ii) Making an observation

Reason — In the scientific method the starting point is the observation of facts; from these observations a hypothesis is then put forward, and it is afterwards tested by experiment.

Note: The textbook’s printed answer key gives option (a), “Formulating a hypothesis.” However, according to the chapter’s explanation and the given case-study passage, the scientific method begins by observing facts. Therefore, the correct answer is option (c), “Making an observation,” and option (a) in the printed answer key is a misprint.

(iii) Frictional force

Reason — Friction is not one of the fundamental forces. It is really a large-scale effect of the electromagnetic interactions between the surfaces in contact.

(iv) By offering explanations for natural phenomena that lead to technological innovations

Reason — By explaining how natural phenomena work, physics makes new technology possible; advances in electronics, in medical equipment and in space instruments all grow out of such understanding.

(v) They are universal and consistent across time and space

Reason — A physical law holds throughout the universe; it does not change from one place or one time to another.

What is physics? Give a brief account of scientific method of gaining knowledge of science.

Answer

The word 'physics' comes from the Greek word Fusis, which means 'nature', and the subject is essentially the study of nature and of natural phenomena. It looks into matter and energy and the ways in which they act on one another, seeking out the basic laws that govern what happens in nature — from the movement of ordinary objects on the earth to the behaviour of atoms and of the universe as a whole.

Scientific knowledge is built up through the scientific method, a systematic procedure carried out in four stages :

1. Observing the facts.
2. Putting forward a theory or hypothesis to account for what has been observed.
3. Testing the predictions that follow from that theory.
4. Modifying the theory wherever it is necessary.

Taken together, these stages make up the scientific method. Should a fresh observation or measurement disagree with an accepted theory, the theory has to be altered, or in some cases replaced by a new one. Working in this way keeps scientific knowledge reliable and firmly tied to evidence.

What are the main forces operative in nature ? Give their characteristic properties and examples.

Answer

Nature is governed by four basic (fundamental) forces : the gravitational, electromagnetic, weak and strong forces.

1. Gravitational force

Characteristic properties :

• It is the mutual attraction that any two separated bodies exert on each other on account of their masses, and it is always attractive, never repulsive.
• Its strength falls off as the inverse square of the distance.
• It acts along the line joining the two bodies, which makes it a central and hence a conservative force.
• It is a long-range force, reaching across very great distances.
• It is the feeblest of all the forces in nature.
• Its field particle is the graviton.

Example : The earth keeps to its orbit around the sun because of the gravitational pull that the sun exerts on it.

2. Electromagnetic force

Characteristic properties :

• It operates between charged bodies and takes in both the electrostatic and the magnetic force.
• It may attract or repel — like charges and like poles push apart, while unlike ones draw together.
• It too obeys the inverse-square law.
• It is a central force and therefore a conservative force.
• It reaches across large distances and is about 10³⁶ times as strong as gravitation.
• Its field particle is the photon; it holds electrons to nuclei to make atoms, joins atoms into molecules, and binds molecules into matter.

Example : The electron is held to the nucleus of an atom by the electromagnetic force.

3. Weak force

Characteristic properties :

• It makes light elementary particles interact with one another and with heavier particles.
• It was first recognised during the study of β-emission from nuclei.
• It is roughly 10²⁶ times as strong as gravitation.
• Its field particle is the neutrino.

Example : In β-emission a neutron inside the nucleus turns into a proton, an electron and an antineutrino under the action of the weak force.

4. Strong force

Characteristic properties :

• Nuclear in origin, it binds the protons and neutrons together within the nucleus; it is basically attractive and appears as n–n, p–p and n–p forces.
• It does not obey the inverse-square law.
• It is non-central, and so non-conservative.
• It is of extremely short range, acting over distances of about 10^-15 m; closer in than this it becomes repulsive.
• It is the strongest force in nature, and its field particle is the π-meson.

Example : It is the strong force that keeps the nucleons packed together inside the atomic nucleus.

State and explain the laws of conservation of mechanical energy, mass plus energy, and charge. Give example of each.

Answer

• Conservation of mechanical energy

When a body moves under a conservative force alone, its mechanical energy — the sum of its kinetic and potential energy — stays unchanged. The energy merely passes back and forth between the two forms, while the total remains fixed.

Example : As a body falls freely under gravity, its potential energy is steadily traded for kinetic energy, yet the sum of the two stays the same throughout the fall.

• Conservation of mass plus energy

Mass and energy were once thought to be conserved separately. Einstein's theory of relativity showed instead that they make up a single conserved quantity, so that the total of mass and energy in the universe is constant. When a body loses a mass Δm, an energy ΔE appears in its place, the two being related by

$\Delta\text E = (\Delta\text m),\text c^2$

where c is the speed of light.

Example : In a nuclear reaction a tiny loss of mass shows up as a very large release of energy.

• Conservation of charge

The net charge of an isolated system never changes; charge can be neither produced nor destroyed, but only shifted from one body to another.

Example : When a glass rod is rubbed with silk, the rod is left positively charged and the silk equally negatively charged, so that the rod-and-silk system carries no net charge either before or after the rubbing.

Explain the connection between conservation laws and symmetry.

Answer

Behind every conservation law there lies a symmetry of nature : whenever a system is left unaffected by some change, a related quantity turns out to be conserved.

• The laws of physics stay the same as time goes by. This sameness in time is tied to the conservation of energy.
• The laws are the same wherever they are applied in space. This sameness from place to place is tied to the conservation of linear momentum.
• Space looks the same in every direction, with no direction singled out. This isotropy of space is tied to the conservation of angular momentum.

In short, the symmetries of time and of space are what give rise to the great conservation laws.