Import Question JSON

Current Question (ID: 16476)

Question:

$\text{A charge } q_1 = 5 \times 10^{-8} \text{ C is kept at } 3 \text{ cm from a charge } q_2 = -2 \times 10^{-8} \text{ C.}$ $\text{The potential energy of the system relative to the potential energy at infinite separation is:}$

Options:

1. $3 \times 10^{-4} \text{ J}$
2. $-3 \times 10^{-4} \text{ J}$
3. $9 \times 10^{-6} \text{ J}$
4. $-9 \times 10^{-6} \text{ J}$

Solution:

$U = 9 \times 10^9 \times \frac{5 \times 10^{-8} \times -2 \times 10^{-8}}{3 \times 10^{-2}} = -3 \times 10^{-4} \text{ J}$ $\text{The potential energy of the system relative to the potential energy at infinite separation: } -3 \times 10^{-4} - 0 = -3 \times 10^{-4} \text{ J}$

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
}