Import Question JSON

Current Question (ID: 20072)

Question:

$\text{A electric dipole is formed by two equal and opposite charges } q \text{ with separation } d. \text{ The charges have same mass } m. \text{ It is kept in a uniform electric field } E. \text{ If it is slightly rotated from its equilibrium orientation, then its angular frequency } \omega \text{ is:}$

Options:

1. $\sqrt{\frac{qE}{2md}}$
2. $\sqrt{\frac{2qE}{md}}$
3. $2\sqrt{\frac{qE}{md}}$
4. $\sqrt{\frac{qE}{md}}$

Solution:

$\text{Hint: } T = 2\pi \sqrt{\frac{1}{pE}}$ $T = 2\pi \sqrt{\frac{1}{pE}} = 2\pi \sqrt{\frac{md^2/2}{qdE}} = 2\pi \sqrt{\frac{md}{2qE}} \Rightarrow \omega = \sqrt{\frac{2qE}{md}}$

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
}