Science for Everyone – Physical Paradoxes and Sophisms

Now we come to a book in the Science for Everyone series which eluded me for years, only to be found with one of my dear friends. This book is Physical Paradoxes and Sophisms by V. N. Lange. Long before I had read about this book in the advertisements on the back pages of other books, but had never a chance to see it. Many of the problems discussed in this book are revealing and take you to deeper levels of understanding about physics. Two similar books that I have read are Surprises in Theoretical Physics and More Surprises in Theoretical Physics by Rudolf Peierls.

From the Preface

This book was written for senior schoolchildren and presents a series of physical paradoxes and sophisms differing in theme and complexity. Some of them were known long ago, yet most are published for the first time. “Sophism” and “paradox” are Greek words. A sophism is an argument, though apparently perfectly correct in form, actually contains an error that makes the final deduction absurd. A well-known sophism is “That which you did not lose, you possess. You have not lost horns, hence you possess them.”

On the contrary, a paradox is a statement that seemingly contradicts common sense, yet in fact is true. For example, as a popular Russian saying contends, “it is a fact, however incredible” that when combining velocities with the same direction, the resultant velocity is smaller than their arithmetic sum (this is one of the inferences of the special theory of relativity).

A study of sophisms and paradoxes need not be thought of as a waste of time. Indeed, they were esteemed by such eminent scientists as Gottfried Leibniz, Leonhard Euler, and Albert Einstein. Einstein was very fastidious about his books, and yet he had a shelf full of books on mathematical jokes and puzzles. Maybe it was his early love of original problems that developed his striking paradoxes has played an extraordinary role in the development of contemporary physics. We hope that this small collection will help its readers avoid making some mistakes. For example, senior schoolchildren and first—year students are often observed, in trying to solve ballistic pendulum problems and the like, finding the system’s velocity following an elastic collision by applying the law of conservation of mechanical energy only. Such mistakes will hardly be made again after studying the sophism in Problem 1.25 (a “violation” of the law of energy conservation).

The first section of the collection contains the problems, the second section gives short solutions. The latter are useful to check your own solutions and in the cases when a problem is difficult to solve on one’s own. The first two editions of the book were so popular that they quickly sold out. It has been translated into Bulgarian, Roumanian, German (two editions in GDR), Japanese, and the languages of the peoples of the USSR. Its success stimulated me to compose new paradoxes and sophisms, thus resulting in the present edition. In preparing it, I have omitted some problems, revised the text and solution of others, and added new ones.

The book was translated from the Russian by Valerii Ilyushchenko and was first published by Mir in 1987.

Thanks AlKaPRo for providing this book.

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Updated: 15 January 2019

Following is the list of contents:


Preface 9
Chapter 1. Mechanics 11
1.1. The Amazing Adventures of a Subway Passenger 11
1.2. Will the Propeller—Driven Sledge Move? 11
1.3. What Is a Boat Velocity? 12
1.4. The Strange Outcome of Combining Velocitie1.5. What is the Average Velocity? 15
1.6. Less Haste, Less Time Waste! 15
1.7. “Notwithstanding” the Law of Inertia 16
1.8. The Weight of a Diesel Locomotive Equals To the Train 16
1.9. Why Are the Ends of the Shafts Lying in RadBearings Tapered? 17
1.10. The Wear on the Cylinder Walls of an Internal Combustion Engine 18
1.11. Rolling Friction Must Vanish 18
1.12. What Is the Force Exerted by a Table’s Legs
1.13. A Mysterious Lever 23
1.14. A Troublesome Reel 24
1.15. Was Aristotle Right? 25
1.16. Will a Bar Move? 25
1.17. What Force Is Applied to a Body? 26
1.18. Two Hand—Ca1·ts 28
1.19. What Is the Acceleration of the Centre of Gravity? 28
1.20. A Swift Cyclist 30
1.21. Following an Example by Muinchhausen 30
1.22. The Enigma of Universal Gravitation Forces1.23. Which High Tides Are Higher? 31
1.24. In What Way Is Work Dependent on Force a Distance? 32
1.25. A “Violation” of the Law of Conservation of Energy 33
1.26. A Mysterious Disappearance of Energy 34
1.27. The Paradox of Rocket Engines 34
1.28. Where Is the Energy Source? 35
1.29. A Hoop and a Hill 35
1.30. Brickwork Paradox 36
1.31. What ls True? 36
1.32. Is This Engine Possible? 37
1.33. Where Will a Car Overturn after a Sudden Turn? 37
1.34. A Simple Derivation of the Pendulum F1.35. Conical Pendulum 40
1.36. Are Transversal Waves Feasible in Liquid
1.37. Do We Hear Interference in This Experiment
1.38. Why Is the Sound Intensified? 43
1.39. Will the Buggy Move? 43
1.40. Why are Submarines Uncomfortable? 4
1.41. Has Water to Press onto Vessel’s Bottom
1.42. Hydrostatic Paradox 46
1.43. A Physicist`s Error 48
1.44. The Mystery of Garret Window. 49
1.45. Why Do Velocities Differ? 50

Chapter 2. Heat And Molecular Physics 51
2.1. Do Sunken Ships Beach the Bottom? 51
2.2. What Is the Temperature at High Altitud2.3. In Spite of the Thermal Laws… 52
2.4. Why Doesn’t Thermal Insulation Help? 52.5. Which Scale Is More Advantageous? 53
2.6. What Is the Source of the Work? 54
2.7. Does a Compressed Gas Possess Potential Energy? 54
2.8. Again Energy Vanishing… 55
2.9. Where does the Energy of the Fuel Burnt in Rocket Disappear? 55
2.10. Can a Body’s Temperature Be Increase
2.11. From What Metal Should a Soldering Iron Be Made? 56
2.12. A Negative Length 56
2.13. Is the Law of the Energy Conservation Valid in All Cases? 57
2.14. The Mystery of Capillary Phenomena 58
2.15. “Clever” Matches 58
2.16. How Is a Wire Drawn? 59
2.17. Boiling Water Cools Down Ice 59
2.18. Why Does Water Evaporate? 60
2.19. An Italian Question 61
2.20. How Can Water Be Boiled More Efficiently
2.21. Is It Possible to Be Burnt by Ice or to Melt Hot Water? 61
2.22. How Much Fuel Will Be Spared? 61
2.23. How Many Heat Capacities Has Iron? 62
2.24. Why Heat Stoves? 63
2.25. Why Is Such a Machine Not Constructed2.26. When Is Car’s Efficiency Higher? 65
2.27. Is Maxwell’s Demon Feasible? 66

Chapter 3. Electricity and Magnetism 68

3.1. Is Coulomb’s Law Valid? 68
3.2. Should a Current Flow Through a Conductor Which Shorts Battery Poles? 69
3.3. Is the Current in a Branch Equal to That in Unbranched Part of the Circuit? 70
3.4. What Current Can an Accumulator Battery Generate? 71
3.5. How Can Galvanometer Readings Be Dec
3.6. Why Did the Current Fall? 72
3.7. What Is the Resistance of an Electric Bulb
3.8. What Will a Voltmeter Indicate? 72
3.9. What Value Must the Resistance Have? 7
3.10. How Much Current Does the Device Co
3.11. The Mystery of Electrolysis 76
3.12. How to Improve the Efficiency of an Electric Bath 76
3.13. Once More about the Conservation of En
3.14. Why Does the Energy in a Capacitor Reside
3.15. A Single-Pole Magnet 79
3.16. Where Is the Energy Source of a Magnet
3.17. Are the Resistances of All Conductors Id
3.18. Does Transformation Ratio Change for able Transformer Load? 82
3.19. At What Voltage Does a Neon Lamp Ign
3.20. Which Ammeter Readings Are Correct?3
3.21. Why in a Series Circuit ls the Current Di
3.22. How Can the Decrease in Temperature Bplained? 85
3.23. Why Is the Magnetic Field Unchanged?
3.24. How to Check Fuses? 86
3.25. Why Did the Lamps Flash? 87
3.26. Why Are the Voltmeter Readings Different? 88
3.27. Six Hectowatts “Are Equal to” Sixty Kilowatts! 89
3.28. The Certificate of an Electric Motor 89
3.29. Will the Capacitor Be Charged? 89
3.30. A Strange Case of Iron Magnetization 90

Chapter 4. Optics and Atomic Structure 92

4.1. A Simple Method of Travelling into the Past 92
4.2. The Overalls of a Metallurgist 93
4.3. Where to Place a Mirror? 93
4.4. An Uncommon “Mirror” 94
4.5. Why Does a Rainbow Happen? 94
4.6. Is It Possible to Increase Illumination Using a Diverging Lens? 95
4.7. The “Vice Versa” Lenses 97
4.8. When Do We Need a Longer Exposure Time in Photography? 97
4.9. A Wonderful Eye 97
4.10. Why Do Wheels Rotate in the “Wrong” Direction? 98
4.11. How Does a Refracting Telescope Work? 98
4.12. Do Astronomers Need Telescopes? 98
4.13. What Aperture Setting Should Be Used? 99
4.14. Is the Construction of Hyperboloid Realizable? 99
4.15. Instead of a Laser 101
4.16. Will the Colour Be Changed? 102
4.17 What Is the True Colour? 103
4.18. An Incident with R. Wood 103
4.19. Negative Light Pressure 104
4.20. Why Do Identically Heated Bodies Glow Differently? 105
4.21. The Paradox of Rulers 105
4.22. The Paradox of the Lever 106
4.23. How Much of Radium Did the Earth Contain When It Was Born? 107
4.24. How Do Cosmic Rays Originate? 109
4.25. Nuclear Reactions and the Law of Mass Conservation 110
4.26. Are There Electrons Inside an Atomic Nucleus? 110

Solutions 112

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11 Responses to Science for Everyone – Physical Paradoxes and Sophisms

  1. somen says:

    dear damitr.
    once again a great job,Iam eagerly waiting for little mathematics library series


    • damitr says:


      Next few books may satisfy some of your hunger for Mathematics, they are Differential Equations in Applications, Problems in Solid Geometry, Problems in Plane Geometry.



  2. manish says:

    dear domitr

    I am not able to download this. The ifile says that there is no such file. Please help.



  3. manish says:

    I am a great fan of russian books, in fact so much so that I have tried to translate many of the mir titles myself to unearth the wealth in physics they have. Kindly do share some if you have them.


    • s.sanjay says:

      mir publishers were a two-way publishing house – they translated important books in other foreign langauages into russian and russian language (i.e. soviet) books into other foreign languages. when you say you have translated mir titles, which books did you translate and into which language?


  4. Ball says:

    This link isn’t working either. Please check.


  5. asd says:

    what more is to come?


  6. CRT says:

    I can’t unzip the pdf file as it shows error .


  7. jay says:

    I m unable to download the book please help


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