Import Question JSON

Current Question (ID: 19562)

Question:

$\text{A rod is fixed at one end and other end is pulled with force } F = 62.8 \text{ kN, Young's modulus of rod is } 2 \times 10^{11} \text{ N/m}^2. \text{ If the radius of cross-section of rod is } 20 \text{ mm the strain produced in rod is}$

Options:

1. $2.5 \times 10^{-3}$
2. $2.5 \times 10^{-4}$
3. $2 \times 10^{-3}$
4. $2 \times 10^{-4}$

Solution:

$\text{Hint: } Y = \frac{F/A}{\Delta l/l}$ $\text{Strain} = \left( \frac{F}{AY} \right) = \frac{62.8 \times 10^3}{3.14 \times (0.02)^2 \times 2 \times 10^{11}} = 2.5 \times 10^{-4}$

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
}