Import Question JSON

Current Question (ID: 20164)

Question:

$\text{The energy stored in the electric field produced by a metal sphere is } 4.5 \text{ J.}$ $\text{If the sphere contains } 4 \, \mu\text{C charge, its radius will be:}$ $\text{(Take: } \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{N} - \text{m}^2/\text{C}^2)$

Options:

1. $28 \, \text{mm}$
2. $32 \, \text{mm}$
3. $20 \, \text{mm}$
4. $16 \, \text{mm}$

Solution:

$\text{Hint: } W = \frac{Q^2}{2C}$

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
}