Relativite — Quiz — Introduction A La Relativite Restreinte

{
  "quiz_title": "Introduction A La Relativite Restreinte",
  "quiz_slug": "01_introduction_a_la_relativite_restreinte_quiz",
  "quiz_description": "Quiz Edu509 : Introduction A La Relativite Restreinte",
  "quiz_settings": {
    "time_limit": {
      "time_value": 0,
      "time_type": "minutes"
    },
    "hide_quiz_time_display": false,
    "attempts_allowed": 0,
    "passing_grade": 70,
    "max_questions_for_answer": 0,
    "questions_order": "rand",
    "hide_question_number_overview": false,
    "short_answer_characters_limit": 200
  },
  "questions": [
    {
      "question_order": 1,
      "question_title": "Quel est le facteur de Lorentz \\\\( \\\\gamma \\\\) pour un objet se déplaçant à \\\\( v = 0{,}8c \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Le facteur de Lorentz est \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - (0{,}8)^2}} = \\\\frac{1}{\\\\sqrt{0{,}36}} = \\\\frac{1}{0{,}6} = 1,67 \\\\).",
      "answers": [
        {
          "answer_title": "1,67",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "2,50",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "1,25",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "0,80",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 2,
      "question_title": "Un vaisseau spatial se déplace à \\\\( v = 0{,}6c \\\\). Si la durée propre d’un événement à bord est \\\\( 2{,}0 \\\\mathrm{s} \\\\), quelle durée mesure un observateur immobile ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La durée mesurée est \\\\( \\\\Delta t = \\\\gamma \\\\Delta t_0 = 1,25 \\\\times 2,0 = 2,5 \\\\) s, avec \\\\( \\\\gamma = 1,25 \\\\) pour \\\\( v = 0,6c \\\\).",
      "answers": [
        {
          "answer_title": "2,5 s",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1,6 s",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3,2 s",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "2,0 s",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 3,
      "question_title": "Quelle est la longueur mesurée d’un train de longueur propre \\\\( 200 \\\\mathrm{m} \\\\) se déplaçant à \\\\( 0{,}8c \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La contraction des longueurs donne \\\\( L = \\\\frac{L_0}{\\\\gamma} = \\\\frac{200}{1,67} \\\\approx 119,8 \\\\) m.",
      "answers": [
        {
          "answer_title": "119,8 m",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "200 m",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "167 m",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "80 m",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 4,
      "question_title": "Laquelle des affirmations suivantes est un postulat de la relativité restreinte ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Un des deux postulats d’Einstein est que la vitesse de la lumière dans le vide est la même pour tous les observateurs, quel que soit leur mouvement.",
      "answers": [
        {
          "answer_title": "La vitesse de la lumière dans le vide est la même pour tous les observateurs.",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "La masse d’un objet ne change jamais.",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Le temps est absolu pour tous les référentiels.",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "La vitesse de la lumière dépend du mouvement de la source.",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 5,
      "question_title": "Un objet se déplace à \\\\( 0{,}99c \\\\). Quel est son facteur de Lorentz \\\\( \\\\gamma \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Pour \\\\( v = 0,99c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - (0,99)^2}} \\\\approx 7,09 \\\\).",
      "answers": [
        {
          "answer_title": "7,09",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "3,21",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "1,41",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "0,99",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 6,
      "question_title": "Quelle est l’énergie totale d’un proton de masse au repos \\\\( 1{,}67 \\\\times 10^{-27} \\\\mathrm{kg} \\\\) accéléré à \\\\( 0{,}99c \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’énergie totale est \\\\( E = \\\\gamma m_0 c^2 = 7,09 \\\\times 1,67 \\\\times 10^{-27} \\\\times 9,00 \\\\times 10^{16} = 1,07 \\\\times 10^{-9} \\\\) J.",
      "answers": [
        {
          "answer_title": "1,07 \\\\times 10^{-9} \\\\mathrm{J}",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1,50 \\\\times 10^{-10} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "9,00 \\\\times 10^{-16} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "7,09 \\\\times 10^{-27} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 7,
      "question_title": "Quelle est l’énergie au repos d’un objet de masse \\\\( 2,0 \\\\mathrm{kg} \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’énergie au repos est \\\\( E = mc^2 = 2,0 \\\\times (3,00 \\\\times 10^8)^2 = 2,0 \\\\times 9,00 \\\\times 10^{16} = 1,8 \\\\times 10^{17} \\\\) J.",
      "answers": [
        {
          "answer_title": "1,8 \\\\times 10^{17} \\\\mathrm{J}",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "6,0 \\\\times 10^{8} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3,0 \\\\times 10^{8} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "2,0 \\\\times 10^{16} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 8,
      "question_title": "Deux événements sont-ils toujours simultanés pour tous les observateurs ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La simultanéité est relative : deux événements simultanés dans un référentiel ne le sont pas forcément dans un autre en mouvement.",
      "answers": [
        {
          "answer_title": "Non",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Oui",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Seulement si les observateurs sont au repos",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Seulement si les événements sont au même endroit",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 9,
      "question_title": "Un vaisseau se déplace à \\\\( 0{,}7c \\\\) et lance une sonde à \\\\( 0{,}5c \\\\) (par rapport au vaisseau). Quelle est la vitesse de la sonde par rapport à la Terre ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’addition relativiste donne \\\\( u = \\\\frac{0,5c + 0,7c}{1 + 0,35} = \\\\frac{1,2c}{1,35} \\\\approx 0,89c \\\\).",
      "answers": [
        {
          "answer_title": "0,89c",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1,2c",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "0,35c",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "0,7c",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 10,
      "question_title": "Quelle est la contraction de longueur d’une barre de \\\\( 5,0 \\\\mathrm{m} \\\\) mesurée à \\\\( v = 0,6c \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Pour \\\\( v = 0,6c \\\\), \\\\( \\\\gamma = 1,25 \\\\). Donc \\\\( L = \\\\frac{5,0}{1,25} = 4,0 \\\\) m.",
      "answers": [
        {
          "answer_title": "4,0 m",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "5,0 m",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3,0 m",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "2,5 m",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 11,
      "question_title": "Un photon a-t-il une masse au repos non nulle ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Le photon a une masse au repos nulle, mais il possède de l’énergie et une quantité de mouvement.",
      "answers": [
        {
          "answer_title": "Non",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Oui",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Seulement à grande vitesse",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Seulement dans le vide",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 12,
      "question_title": "Quelle est la différence d’âge entre deux jumeaux si l’un voyage à \\\\( 0,95c \\\\) vers une étoile distante de 6 années-lumière (aller-retour) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La différence d’âge est \\\\( 12,63 - 3,94 = 8,69 \\\\) ans, calculée avec la dilatation du temps.",
      "answers": [
        {
          "answer_title": "8,69 ans",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "12,63 ans",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3,94 ans",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "6,00 ans",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 13,
      "question_title": "Quelle est la formule correcte pour la transformation de Lorentz de la position \\\\( x' \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La transformation de Lorentz pour la position est \\\\( x' = \\\\gamma (x - vt) \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( x' = \\\\gamma (x - vt) \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( x' = x + vt \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( x' = \\\\gamma (x + vt) \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( x' = x - vt \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 14,
      "question_title": "Quelle est la vitesse de la lumière dans le vide ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La vitesse de la lumière dans le vide est \\\\( c = 3,00 \\\\times 10^8 \\\\) m/s.",
      "answers": [
        {
          "answer_title": "3,00 \\\\times 10^8 m/s",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1,50 \\\\times 10^8 m/s",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3,00 \\\\times 10^6 m/s",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "9,81 \\\\times 10^8 m/s",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 15,
      "question_title": "Si un objet a une énergie totale de \\\\( 5,0 \\\\times 10^{10} \\\\mathrm{J} \\\\) et une énergie au repos de \\\\( 2,0 \\\\times 10^{10} \\\\mathrm{J} \\\\), quelle est son énergie cinétique ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’énergie cinétique relativiste est \\\\( E_c = E - E_0 = 5,0 \\\\times 10^{10} - 2,0 \\\\times 10^{10} = 3,0 \\\\times 10^{10} \\\\) J.",
      "answers": [
        {
          "answer_title": "3,0 \\\\times 10^{10} \\\\mathrm{J}",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "7,0 \\\\times 10^{10} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "2,5 \\\\times 10^{10} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "1,0 \\\\times 10^{10} \\\\mathrm{J}",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 16,
      "question_title": "Dans la contraction des longueurs, quelle grandeur reste constante ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La longueur propre \\\\( L_0 \\\\) est la longueur mesurée dans le référentiel de l’objet, elle ne change pas.",
      "answers": [
        {
          "answer_title": "La longueur propre \\\\( L_0 \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "La longueur mesurée \\\\( L \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "La vitesse de l’objet",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Le facteur de Lorentz",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 17,
      "question_title": "Quelle est la formule de l’addition relativiste des vitesses ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La formule correcte est \\\\( u' = \\\\frac{u + v}{1 + \\\\frac{uv}{c^2}} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( u' = \\\\frac{u + v}{1 + \\\\frac{uv}{c^2}} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( u' = u + v \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( u' = \\\\frac{u - v}{1 - \\\\frac{uv}{c^2}} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( u' = \\\\frac{u + v}{1 - \\\\frac{uv}{c^2}} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 18,
      "question_title": "Un objet se déplace à \\\\( 0,5c \\\\). Quelle est la valeur de \\\\( \\\\gamma \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Pour \\\\( v = 0,5c \\\\), \\\\( \\\\gamma = \\\\frac{1}{\\\\sqrt{1 - 0,25}} = \\\\frac{1}{0,866} = 1,15 \\\\).",
      "answers": [
        {
          "answer_title": "1,15",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1,25",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "1,41",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "2,00",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 19,
      "question_title": "Si la durée propre d’un événement est \\\\( 10 \\\\mathrm{s} \\\\) et \\\\( \\\\gamma = 2 \\\\), quelle est la durée mesurée par un observateur immobile ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La durée mesurée est \\\\( \\\\Delta t = \\\\gamma \\\\Delta t_0 = 2 \\\\times 10 = 20 \\\\) s.",
      "answers": [
        {
          "answer_title": "20 s",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "5 s",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "10 s",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "15 s",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 20,
      "question_title": "Un objet de longueur propre \\\\( 100 \\\\mathrm{m} \\\\) se déplace à \\\\( 0,6c \\\\). Quelle longueur mesure un observateur immobile ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Pour \\\\( v = 0,6c \\\\), \\\\( \\\\gamma = 1,25 \\\\). Donc \\\\( L = \\\\frac{100}{1,25} = 80 \\\\) m.",
      "answers": [
        {
          "answer_title": "80 m",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "100 m",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "60 m",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "125 m",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    }
  ]
}