Import Question JSON

Current Question (ID: 10732)

Question:

$\text{A metal bar of length } L \text{ and area of cross-section } A \text{ is clamped between two rigid supports. For the material of the rod, it's Young's modulus is } Y \text{ and the coefficient of linear expansion is } \alpha. \text{ If the temperature of the rod is increased by } \Delta t°C, \text{ the force exerted by the rod on the supports will be:}$

Options:

1. $YAL\Delta t$
2. $YA\alpha\Delta t$ (Correct)
3. $\frac{YL\alpha\Delta t}{A}$
4. $Y\alpha AL\Delta t$

Solution:

$\Delta L = L\alpha \Delta T$ $Y = \frac{\sigma}{\varepsilon} = \frac{F/A}{\Delta L/L}$ $F = YA\frac{\Delta L}{L} = YA\frac{L\alpha\Delta T}{L} = Y\alpha A \Delta T$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}