Import Question JSON

Current Question (ID: 20191)

Question:

$\text{Two charges (both at rest initially), having a charge } Q \text{ and } -Q \text{ are released from the situation shown. If the kinetic energy of the system when the separation between them becomes half, is } \frac{1}{4\pi\varepsilon_0} \frac{Q^2}{nr_0}. \text{ Then } n =?$

Options:

1. 2
2. 3 (Correct)
3. 1
4. 4

Solution:

$\text{Initial potential energy } U_i = -\frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0}$ $\text{Final potential energy } U_f = -\frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0/2}$ $\text{Loss in potential energy, } U_i - U_f = -\frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0} + \frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0/2} = \frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0}$ $\text{Kinetic energy } = \frac{1}{4\pi\varepsilon_0} \times \frac{Q^2}{r_0}$ $n = 1$

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
}