Import Question JSON

Current Question (ID: 19549)

Question:

$\text{A sphere of small size is at the bottom of a lake of depth } 200 \text{ m. Due to pressure its fractional change in volume is } \alpha \times 10^{-7}. \text{ What is the value of } \alpha, \text{ if the bulk modulus of the sphere is } 5 \times 10^{12} \text{ Pa? (Use } g = 10 \text{ m/s}^2)$

Options:

1. $5$
2. $4$
3. $6$
4. $10$

Solution:

$\text{Hint: } B = -\frac{\Delta P}{\left(\frac{\Delta V}{V}\right)}$ $B = \left|\frac{\Delta P}{\frac{\Delta V}{V}}\right|$ $\left|\frac{\Delta V}{V}\right| = \frac{\left|\Delta P\right|}{B} = \frac{h \rho g}{B} = \frac{200 \times 10^3 \times 10}{5 \times 10^{12}} = 40 \times 10^{-8}$ $= 4 \times 10^{-7}$ $\Rightarrow \alpha = 4$

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
}