Import Question JSON

Current Question (ID: 10407)

Question:

$\text{A ball falling into a lake of depth 200 m shows a 0.1\% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?}$

Options:

1. $19.6 \times 10^8 \text{ N/m}^2$
2. $19.6 \times 10^{-10} \text{ N/m}^2$
3. $19.6 \times 10^{10} \text{ N/m}^2$
4. $19.6 \times 10^{-8} \text{ N/m}^2$

Solution:

\text{The bulk modulus is defined as: } B = \Delta p / (\Delta V / V) \text{Where:} \Delta p = \text{change in pressure} = h \rho g = 200 \times 10^3 \times 9.8 = 1.96 \times 10^6 \text{ Pa} \Delta V / V = \text{fractional change in volume} = 0.1\% = 0.001 \text{Therefore:} B = (1.96 \times 10^6) / (0.001) = 1.96 \times 10^9 \text{ N/m}^2

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
}