Import Question JSON

Current Question (ID: 10379)

Question:

$\text{An elastic material of Young's modulus } Y \text{ is subjected to a stress } S. \text{ The elastic energy stored per unit volume of the material is:}$

Options:

1. $\frac{SY}{2}$
2. $\frac{S^2}{2Y}$
3. $\frac{S}{2Y}$
4. $\frac{2S}{Y}$

Solution:

\text{Energy stored in the wire per unit volume,} u = \frac{1}{2} \times \text{stress} \times \text{strain} \text{also, strain} = \frac{\text{stress}}{Y} \text{As } u = \frac{1}{2} \times \text{stress} \times \frac{\text{stress}}{Y} = \frac{1}{2} \times \frac{S^2}{Y} = \frac{S^2}{2Y}

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
}