**Newton’s laws of motion** are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn’t exist. These three laws have been expressed in several ways, over nearly three centuries,and can be summarised as follows:

First law: |
In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.^{} |

Second law: |
In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant – see below.) |

Third law: |
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. |

The three laws of motion were first compiled by Isaac Newton in his *Philosophiæ Naturalis Principia Mathematica* (*Mathematical Principles of Natural Philosophy*), first published in 1687.Newton used them to explain and investigate the motion of many physical objects and systems For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler’s laws of planetary motion.

A **fourth law** is often also described in the bibliography, which states that forces add up like vectors, that is, that forces obey the principle of superposition.^{}

Newton’s laws are applied to objects which are idealised as single point masses,in the sense that the size and shape of the object’s body are neglected to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star.

In their original form, Newton’s laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newton’s laws of motion for rigid bodies called Euler’s laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton’s laws of motion, then Euler’s laws can be derived from Newton’s laws. Euler’s laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure.

Newton’s laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law holds only when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second The explicit concept of an inertial frame of reference was not developed until long after Newton’s death.

In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities.

Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light^{}

The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object’s speed and the direction of its motion; therefore, the statement that the object’s velocity is constant is a statement that both its speed and the direction of its motion are constant.

The first law can be stated mathematically when the mass is a non-zero constant, as,

- {\displaystyle \sum \mathbf {F} =0\;\Leftrightarrow \;{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=0.}

Consequently,

- An object that is at rest will stay at rest unless a force acts upon it.
- An object that is in motion will not change its velocity unless a force acts upon it.

This is known as *uniform motion*. An object *continues* to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skilfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continuously move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speedNewton’s first law is often referred to as the *law of inertia*. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as:

In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it^{}

Newton’s first and second laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity.

The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.

- {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}={\frac {\mathrm {d} (m\mathbf {v} )}{\mathrm {d} t}}.}

The second law can also be stated in terms of an object’s acceleration. Since Newton’s second law is valid only for constant-mass systems,*m* can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,

- {\displaystyle \mathbf {F} =m\,{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}=m\mathbf {a} ,}

where **F** is the net force applied, *m* is the mass of the body, and **a** is the body’s acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it. An application of this notation is the derivation of G Subscript C.

Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.

Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).

Newton’s second law is an approximation that is increasingly worse at high speeds because of relativistic effects.

An impulse **J** occurs when a force **F** acts over an interval of time Δ*t*, and it is given by^{}

- {\displaystyle \mathbf {J} =\int _{\Delta t}\mathbf {F} \,\mathrm {d} t.}

Since force is the time derivative of momentum, it follows that

- {\displaystyle \mathbf {J} =\Delta \mathbf {p} =m\Delta \mathbf {v} .}

This relation between impulse and momentum is closer to Newton’s wording of the second law.

Impulse is a concept frequently used in the analysis of collisions and impacts.

Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law; that is, the following formula is wrong^{}

- {\displaystyle \mathbf {F} _{\mathrm {net} }={\frac {\mathrm {d} }{\mathrm {d} t}}{\big [}m(t)\mathbf {v} (t){\big ]}=m(t){\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}+\mathbf {v} (t){\frac {\mathrm {d} m}{\mathrm {d} t}}.\qquad \mathrm {(wrong)} }

The falsehood of this formula can be seen by noting that it does not respect Galilean invariance: a variable-mass object with **F** = 0 in one frame will be seen to have **F** ≠ 0 in another frame.The correct equation of motion for a body whose mass *m* varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected/accreted mass; the result is

- {\displaystyle \mathbf {F} +\mathbf {u} {\frac {\mathrm {d} m}{\mathrm {d} t}}=m{\mathrm {d} \mathbf {v} \over \mathrm {d} t}}

where **u** is the velocity of the escaping or incoming mass relative to the body. From this equation one can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation. Under some conventions, the quantity **u** d*m*/d*t* on the left-hand side, which represents the advection of momentum, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity **F**. Then, by substituting the definition of acceleration, the equation becomes **F** = *m***a**.

The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object *A* exerts a force **F**_{A}on a second object *B*, then *B* simultaneously exerts a force **F**_{B} on *A*, and the two forces are equal in magnitude and opposite in direction: **F**_{A} = −**F**_{B}.The third law means that all forces are *interactions* between different bodies,or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body A; the force exerted by Body A on Body B is called the “action”, and the force exerted by Body B on Body A is called the “reaction”. This law is sometimes referred to as the *action-reaction law*, with **F**_{A} called the “action” and **F**_{B} the “reaction”. In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn’t necessary to identify one force as the “action” and the other as the “reaction”. The action and the reaction are simultaneous, and it does not matter which is called the *action* and which is called *reaction*; both forces are part of a single interaction, and neither force exists without the other^{}

The two forces in Newton’s third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car’s tires, then it is also a frictional force that Newton’s third law predicts for the tires pushing backward on the road).

From a conceptual standpoint, Newton’s third law is seen when a person walks: they push against the floor, and the floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes back on the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with the water, pushing the water backward, while the water simultaneously pushes the person forward—both the person and the water push against each other. The reaction forces account for the motion in these examples. These forces depend on friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force.

From the original Latin of Newton’s *Principia*:

“ | Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. |
” |

Translated to English, this reads:

“ | Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. | ” |

The ancient Greek philosopher Aristotle had the view that all objects have a natural place in the universe: that heavy objects (such as rocks) wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed continually to propel it, otherwise it would stop moving. Galileo Galilei, however, realised that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. In other words, Galileo stated that, in the *absence* of a force, a moving object will continue moving. (The tendency of objects to resist changes in motion was what Johannes Kepler had called *inertia*.) This insight was refined by Newton, who made it into his first law, also known as the “law of inertia”—no force means no acceleration, and hence the body will maintain its velocity. As Newton’s first law is a restatement of the law of inertia which Galileo had already described, Newton appropriately gave credit to Galileo.

The law of inertia apparently occurred to several different natural philosophers and scientists independently, including Thomas Hobbes in his *Leviathan*. The 17th century philosopher and mathematician René Descartes also formulated the law, although he did not perform any experiments to confirm it.^{}

Newton’s original Latin reads:

“ | Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur. |
” |

This was translated quite closely in Motte’s 1729 translation as:

“ | Law II: The alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d. | ” |

According to modern ideas of how Newton was using his terminology this is understood, in modern terms, as an equivalent of:

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

This may be expressed by the formula F = p’, where p’ is the time derivative of the momentum p. This equation can be seen clearly in the Wren Library of Trinity College, Cambridge, in a glass case in which Newton’s manuscript is open to the relevant page.

Motte’s 1729 translation of Newton’s Latin continued with Newton’s commentary on the second law of motion, reading:

If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton’s formulation and modern formulations^{}

“ | Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi. |
” |

Translated to English, this reads:

“ | Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. | ” |

Newton’s Scholium (explanatory comment) to this law:

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.

In the above, as usual, *motion* is Newton’s name for momentum, hence his careful distinction between motion and velocity.

Newton used the third law to derive the law of conservation of momentum;from a deeper perspective, however, conservation of momentum is the more fundamental idea (derived via Noether’s theorem from Galilean invariance), and holds in cases where Newton’s third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics.

Newton’s laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton’s laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.

These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton’s laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds (in special relativity, the Lorentz factor must be included in the expression for momentum along with the rest mass and velocity) or very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory.

In quantum mechanics, concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton’s laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form **F** = d**p**/d*t*, where **F** and **p** are four-vectors.

In modern physics, the laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton’s laws, since they apply to both light and matter, and to both classical and non-classical physics.

This can be stated simply, “Momentum, energy and angular momentum cannot be created or destroyed.”

Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forcesoriginate out of exchange by virtual particles. Other forces, such as gravity and fermionic degeneracy pressure, also arise from the momentum conservation. Indeed, the conservation of 4-momentum in inertial motion via curved space-time results in what we call gravitational force in general relativity theory. The application of the space derivative (which is a momentum operator in quantum mechanics) to the overlapping wave functions of a pair of fermions (particles with half-integer spin) results in shifts of maxima of compound wavefunction away from each other, which is observable as the “repulsion” of the fermions.

Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this action at a distance, and it was in this context that he stated the famous phrase “I feign no hypotheses“. In modern physics, action at a distance has been completely eliminated, except for subtle effects involving quantum entanglement. (In particular, this refers to Bell’s theorem – that no local model can reproduce the predictions of Quantum Theory.) Despite only being an approximation, in modern engineering and all practical applications involving the motion of vehicles and satellites, the concept of action at a distance is used extensively.

The discovery of the second law of thermodynamics by Carnot in the 19th century showed that not every physical quantity is conserved over time, thus disproving the validity of inducing the opposite metaphysical view from Newton’s laws. Hence, a “steady-state” worldview based solely on Newton’s laws and the conservation laws does not take entropy into account.

12th class is a no risk class. It is the class which decide your future. Whether you are going to work in MNC or going to work with usual private firms, it all depends here. To ensure the good marks to students we always stands behind them with all practical and theoretical support on Physics investigatory project. These Physics investigatory projects are usually have to be made by all students with physics and to be shown in boards practical. We at Gurukul Technicals Institute provide every student the theory behind the projects and give all possible required material to make the project work successfully. We duly provide equipped lab with latest lab materials. Conductors and Semiconductors are provided with Circuit diagram so that student can make project easily. Students make projects such as Full wave rectifier, Half wave rectifier, Fire alarm, rain alarm, Electromagnetic Induction, Logic gates(AND gate, OR gate, NOT gate, XAND gate, XNOR gate), Transistor as switch, Transistor as amplifier, Charging and Discharging of Capacitors, Series and Parallel Resistance etc etc. Students also get help on making these above given projects to made on cardboard or on breadboard as instructed by teacher. Students are also welcome to take help on report on given physics investigatory projects. After reading this website you can also send this information to your friend or relative studying in 12th class so it will make useful to him/her.

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**Physics Projects with Reports:**

- TO CONSTRUCT A CIRCUIT FOR TOUCH ALARM.
- EDDY CURRENT {WITHOUT MODEL }
- PHOTOCONDUCTIVE CELL
- MUTUAL INDUCTION
- TO STUDY NPN-TRANSISTOR AMPLIFIER
- TO CONSTRUCT A ELECTRIC MOTORS (D.C.MOTOR)
- TO STUDY HOW A TRANSISTOR AMPLIFIER WORK ‘PNP’ AMPLIFIER TRANSISTOR.
- HOUSEHOLD CIRCUITS
- AC TO DC CONVERTER (FULL WAVE RECTIFIER)
- AC TO DC CONVERTER (HALF WAVE RECTIFIER)
- TO CONSTRUCT A CIRCUIT OF FENCE WIRE BURGLAR ALARM
- TO SHOW THE PRINCIPLE OF FARADAY’S AND A.C. GENERATOR.
- THERMOCOUPLE
- TO STUDY FARADAY’S LAWS-TO FIND THE CHARGE ON AN ELECTRON
- FARADAY’S LAW’S OF ELECTROLYSIS
- TO STUDY A POSITIVE FEED BACK CIRCUIT OF AN AUDIO OSCILLATOR (LC OSCILLATOR)
- HOW DOES AN ELECTRIC GENERATOR WORK
- TO SHOW THAT A SOLENOID CARRYING AN ELECTRIC CURRENT PRODUCES A MAGNETIC FIELD SIMILAR TO THAT PRODUCED BY A BAR MAGNET.
- ELECTROCHEMICAL CELL (PRIMARY CELL)
- BOOLAN LOGIC GATE
- TO STUDY THE CHARGE AND DISCHARGING OF CAPACITOR IN SERIES
- WORKING OF POTENTIOMETER
- KIRCHOFF’S LAW
- TO DEMONSTRATE THE WORKING OF AN ELECTROLYTIC CAPACITOR BY MEANS OF ITS CHARGING AND DISCHARGING WITH THE HELP OF AN AUDIO OSCILLATOR AND TO STUDY AND COMPARE THE TWO CAPACITORS UNDER SERIES AND PARALLEL COMBINATION.(Z)
- RADIOACTIVITY AND NUCLEAR REACTIONS.
- RADIOISOTOPE THERMOELECTRIC GENERATOR.
- TO CONSTRUCT A CIRCUIT OF SOUND OPERATED SWITCH.
- TO CONSTRUCT A CIRCUIT OF TIME OPERATED SWITCH.
- TO CONSTRUCT A CIRCUIT OF SOUND AMPLIFIER.
- TO CONSTRUCT A CIRCUIT OF A FIRE ALARM.
- TO CONSTRUCT A CIRCUIT OF CLAP SWITCH.
- TO CONSTRUCT A CIRCUIT OF TRANSISTOR SWITCH
- TO FIND OUT OPTICAL ACTIVITY ARISES WHEN THE POLARIZATION AXIS OF LIGHT IS ROTATED AS IT PASSES THROUGH A SUBSTANCE
- PUSH-PULL AMPLIFIER
- HARTLEY OSCILLATORS
- PUSH PULL AMPLIFIER
- REPORT ON MAGNETIC FIELDS, MAGNETIC FORCES, AND ELECTROMAGNETIC INDUCTION LAWS OF REFRACTION (Z).
- RAY OPTICS-TO FIND REFRACTIVE INDEX OF THE MATERIAL OF THE PRISM BY TOTAL INTERNAL REFRACTION (Z).
- TO DEMONSTRATE THE WORKING OF AN ELECTROLYTIC CAPACITOR BY MEANS OF ITS CHARGING AND DISCHARGING WITH THE HELP OF AN AUDIO OSCILLATOR AND TO STUDY AND COMPARE THE TWO CAPACITORS UNDER SERIES AND PARALLEL COMBINATIONS.
- TO STUDY THE EFFECT OF THE DIAMETER AND THE NUMBER OF TURNS OF THE SPRING ON ITS STRENGTH HAS BEEN INVESTIGATION IN THIS STUDY.(Z)
- TO FIND OUT THE THERMAL COEFFICIENT OF RESISTANCE FOR A DIVAN SET OF WIRES AND THUS SUGGEST THE WIRE IN WHICH ENERGY LOSS DUE TO HEAT GENERATION IS MINIMUN.(Z)
- TO SEE THAT WATER CONDUCTS ELECTRICITY BETTER WHEN IMPURITIES ARE ADDED IT. (Z)
- TO MAKE NOR GATE WITH THE COMBINATION OF TWO GATES. (Z)
- PASCAL’S LAW AND ITS APPLICATIONS
- BRIDGE RECTIFIER- A CIRCUIT USING FOUR DIODES TO PROVIDE FULL WAVE RECTIFICATION.CONVERTS AN AC VOLTAGE TO A PULSATING DC VOLTAGE.
- TO CONSTRUCT A CIRCUIT OF QUIZ BUZZER.
- TO CONSTRUCT A CIRCUIT OF LASER SECURITY SYSTEM.
- TO CONSTRUCT A CIRCUIT OF RAIN ALARM.
- TO CONSTRUCT A CIRCUIT OF WATER LEVEL INDICATOR.
- THE EFFECT OF TEMPERATURE ON DISPOSABLE AND NON DISPOSABLE BATTERIES
- TO INVESTIGATE THE EFFECT OF THE FOLLOWING FACTORS ON THE INTERNAL RESISTANCE OF A LACLANCHE CELL.
- TO CONSTRUCT A CIRCUIT OF OPTICAL SWITCHING.
- TO CONSTRUCT A CIRCUIT OFCAPACITOR CHARGE OSCILATOR
- TO CONSTRUCT A CIRCUIT OFCAPACITOR STORAGE LED
- TO CONSTRUCT A CIRCUIT OF TWO TRANSISTOR OSCILLATOR
- EXPERIMENTS IN ELECTROCHEMISTRY
- TO SHOW THE UNIDIRECTION ACTION OF DIODE
- OPTICAL FIBER COMMUNICATION
- TO CONSTRUCT A CIRCUIT OF ELECTRONIC EYE

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