{
    "1": {
        "pid": "1",
        "question": "When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as being constant. Integration sums the work done in all those parts. Here we use the generic result of the integration.\r\n\r\nIn Figure, a cumin canister of mass $m=0.40 \\mathrm{~kg}$ slides across a horizontal frictionless counter with speed $v=0.50 \\mathrm{~m} / \\mathrm{s}$. It then runs into and compresses a spring of spring constant $k=750 \\mathrm{~N} / \\mathrm{m}$. When the canister is momentarily stopped by the spring, by what distance $d$ is the spring compressed?",
        "image": "images/1.jpg",
        "choices": null,
        "unit": null,
        "precision": 1.0,
        "answer": "1.2",
        "question_type": "free_form",
        "answer_type": "float",
        "metadata": {
            "category": "math-targeted-vqa",
            "context": "scientific figure",
            "grade": "college",
            "img_height": 720,
            "img_width": 1514,
            "language": "english",
            "skills": [
                "scientific reasoning"
            ],
            "source": "SciBench",
            "split": "testmini",
            "task": "textbook question answering"
        },
        "query": "Hint: Please answer the question requiring a floating-point number with one decimal place and provide the final value, e.g., 1.2, 1.3, 1.4, at the end.\nQuestion: When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as being constant. Integration sums the work done in all those parts. Here we use the generic result of the integration.\r\n\r\nIn Figure, a cumin canister of mass $m=0.40 \\mathrm{~kg}$ slides across a horizontal frictionless counter with speed $v=0.50 \\mathrm{~m} / \\mathrm{s}$. It then runs into and compresses a spring of spring constant $k=750 \\mathrm{~N} / \\mathrm{m}$. When the canister is momentarily stopped by the spring, by what distance $d$ is the spring compressed?",
        "response": "To find the distance \\( d \\) that the spring is compressed, we can use the principle of conservation of energy. The kinetic energy of the canister is converted into the potential energy stored in the compressed spring.\n\nThe initial kinetic energy \\( K \\) of the canister is given by:\n\\[ K = \\frac{1}{2}mv^2 \\]\n\nThe potential energy \\( U \\) stored in the compressed spring is given by:\n\\[ U = \\frac{1}{2}kd^2 \\]\n\nAt the moment the canister is stopped, all its kinetic energy is converted into the potential energy of the spring:\n\\[ K = U \\]\n\nSubstituting the expressions for \\( K \\) and \\( U \\):\n\\[ \\frac{1}{2}mv^2 = \\frac{1}{2}kd^2 \\]\n\nSolving for \\( d \\):\n\\[ d^2 = \\frac{mv^2}{k} \\]\n\\[ d = \\sqrt{\\frac{mv^2}{k}} \\]\n\nGiven:\n- \\( m = 0.40 \\, \\text{kg} \\)\n- \\( v = 0.50 \\, \\text{m/s} \\)\n- \\( k = 750 \\, \\text{N/m} \\)\n\nSubstitute the values:\n\\[ d = \\sqrt{\\frac{(0.40 \\, \\text{kg})(0.50 \\, \\text{m/s})^2}{750 \\, \\text{N/m}}} \\]\n\\[ d = \\sqrt{\\frac{(0.40)(0.25)}{750}} \\]\n\\[ d = \\sqrt{\\frac{0.10}{750}} \\]\n\\[ d = \\sqrt{0.00013333} \\]\n\\[ d \\approx 0.0115 \\, \\text{m} \\]\n\nTherefore, the distance \\( d \\) that the spring is compressed is approximately \\( 0.0115 \\, \\text{m} \\)."
    },
    "2": {
        "pid": "2",
        "question": "what is the total volume of the measuring cup?",
        "image": "images/2.jpg",
        "choices": null,
        "unit": "g",
        "precision": null,
        "answer": "1000",
        "question_type": "free_form",
        "answer_type": "integer",
        "metadata": {
            "category": "general-vqa",
            "context": "natural image",
            "grade": "daily life",
            "img_height": 768,
            "img_width": 1024,
            "language": "english",
            "skills": [
                "numeric commonsense",
                "arithmetic reasoning"
            ],
            "source": "TextVQA",
            "split": "testmini",
            "task": "visual question answering"
        },
        "query": "Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.\nQuestion: what is the total volume of the measuring cup? (Unit: g)",
        "response": "The total volume of the measuring cup is 1000 grams."
    },
    "3": {
        "pid": "3",
        "question": "△ABC的两内角平分线OB、OC相交于点O，若∠A＝110°，则∠BOC＝（）",
        "image": "images/3.jpg",
        "choices": [
            "135°",
            "140°",
            "145°",
            "150°"
        ],
        "unit": null,
        "precision": null,
        "answer": "145°",
        "question_type": "multi_choice",
        "answer_type": "text",
        "metadata": {
            "category": "math-targeted-vqa",
            "context": "geometry diagram",
            "grade": "high school",
            "img_height": 60,
            "img_width": 131,
            "language": "chinese",
            "skills": [
                "geometry reasoning",
                "algebraic reasoning"
            ],
            "source": "GeoQA+",
            "split": "testmini",
            "task": "geometry problem solving"
        },
        "query": "Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: △ABC的两内角平分线OB、OC相交于点O，若∠A＝110°，则∠BOC＝（）\nChoices:\n(A) 135°\n(B) 140°\n(C) 145°\n(D) 150°",
        "response": "To find the measure of ∠BOC, we can use the fact that the sum of the angles in a triangle is 180°. Since OB and OC are the angle bisectors of ∠ABC and ∠ACB respectively, we can find the measure of ∠BOC by subtracting the sum of the measures of ∠ABC and ∠ACB from 180°.\n\nGiven that ∠A = 110°, we can find the sum of ∠ABC and ∠ACB as follows:\n\n∠ABC + ∠ACB = 180° - ∠A\n∠ABC + ∠ACB = 180° - 110°\n∠ABC + ∠ACB = 70°\n\nNow, since OB and OC are angle bisectors, we have:\n\n∠OBC = ∠ABC / 2\n∠OCB = ∠ACB / 2\n\nTherefore, the measure of ∠BOC is:\n\n∠BOC = 180° - (∠OBC + ∠OCB)\n∠BOC = 180° - (∠ABC / 2 + ∠ACB / 2)\n∠BOC = 180° - (∠ABC + ∠ACB) / 2\n∠BOC = 180° - 70° / 2\n∠BOC = 180° - 35°\n∠BOC = 145°\n\nTherefore, the answer is (C)."
    },
    "4": {
        "pid": "4",
        "question": "Subtract all large rubber spheres. Subtract all big shiny cylinders. How many objects are left?",
        "image": "images/4.jpg",
        "choices": null,
        "unit": null,
        "precision": null,
        "answer": "4",
        "question_type": "free_form",
        "answer_type": "integer",
        "metadata": {
            "category": "math-targeted-vqa",
            "context": "synthetic scene",
            "grade": "elementary school",
            "img_height": 240,
            "img_width": 320,
            "language": "english",
            "skills": [
                "geometry reasoning",
                "arithmetic reasoning"
            ],
            "source": "CLEVR-Math",
            "split": "testmini",
            "task": "math word problem"
        },
        "query": "Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, 3, at the end.\nQuestion: Subtract all large rubber spheres. Subtract all big shiny cylinders. How many objects are left?",
        "response": "4"
    },
    "5": {
        "pid": "5",
        "question": "Find $m\\angle H$",
        "image": "images/5.jpg",
        "choices": [
            "97",
            "102",
            "107",
            "122"
        ],
        "unit": null,
        "precision": null,
        "answer": "97",
        "question_type": "multi_choice",
        "answer_type": "text",
        "metadata": {
            "category": "math-targeted-vqa",
            "context": "geometry diagram",
            "grade": "high school",
            "img_height": 245,
            "img_width": 322,
            "language": "english",
            "skills": [
                "geometry reasoning",
                "algebraic reasoning"
            ],
            "source": "Geometry3K",
            "split": "testmini",
            "task": "geometry problem solving"
        },
        "query": "Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find $m\\angle H$\nChoices:\n(A) 97\n(B) 102\n(C) 107\n(D) 122",
        "response": "To find the measure of angle $H$, we first need to understand that the sum of the interior angles of a pentagon is given by the formula $(n-2) \\times 180^\\circ$, where $n$ is the number of sides. For a pentagon, $n=5$, so the sum of the interior angles is $(5-2) \\times 180^\\circ = 3 \\times 180^\\circ = 540^\\circ$.\n\nGiven the angles at vertices $E$, $F$, $G$, $H$, and $J$ as $(x+20)^\\circ$, $(x+5)^\\circ$, $(x+5)^\\circ$, $(x-5)^\\circ$, and $(x+10)^\\circ$ respectively, we can set up the equation:\n\n\\[\n(x+20) + (x+5) + (x+5) + (x-5) + (x+10) = 540\n\\]\n\nSimplifying the left side:\n\n\\[\n5x + 40 = 540\n\\]\n\nSubtracting 40 from both sides:\n\n\\[\n5x = 500\n\\]\n\nDividing by 5:\n\n\\[\nx = 100\n\\]\n\nNow, we can find the measure of angle $H$:\n\n\\[\nH = x - 5 = 100 - 5 = 95^\\circ\n\\]\n\nHowever, this does not match any of the given options. Let's recheck the problem statement and the options provided. It seems there might be a mistake in the options or the problem statement. The correct measure of angle $H$ based on the calculation is $95^\\circ$, but since this is not an option, we should consider the closest match or re-evaluate the problem.\n\nGiven the options, the closest match to $95^\\circ$ is (A) 97. Therefore, the correct answer is:\n\nAnswer: A"
    }
}