Import Question JSON

Current Question (ID: 19560)

Question:

$\text{Choose the option showing the correct relation between Poisson's ratio } (\sigma), \text{ Bulk modulus } (B), \text{ and Modulus of rigidity } (G).$

Options:

1. $\sigma = \frac{3B - 2G}{2G + 6B}$
2. $\sigma = \frac{6B + 2G}{3B - 2G}$
3. $\sigma = \frac{3B - 2G}{9BG}$
4. $B = \frac{3\sigma - 3G}{6\sigma + 2G}$

Solution:

$E = 2G(1 + \sigma) \quad \ldots \ldots \quad (1)$ $E = 3B(1 - 2\sigma) \quad \ldots \ldots \quad (2)$ $1 = \frac{2G}{3B} \left( \frac{1 + \sigma}{1 - 2\sigma} \right)$ $3B - 6B\sigma = 2G + 2G\sigma$ $3B - 2G = \sigma(2G + 6B) \sigma = \frac{3B - 2G}{2G + 6B}$

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
}