Import Question JSON

Current Question (ID: 16889)

Question:

$\text{The bar magnet } A \text{ of magnetic moment } M_A \text{ is found to oscillate at a frequency twice that of magnet } B \text{ of magnetic moment } M_B \text{ and the same moment of inertia when placed in a vibration magnetometer. We may say that:}$

Options:

1. $M_B = 8M_A$
2. $M_A = 4M_B$
3. $M_A = 8M_B$
4. $M_A = 2M_B$

Solution:

$\text{Frequency of oscillation of a bar magnet,}$ $\nu = \frac{1}{2\pi} \sqrt{\frac{M_B}{I}}$ $\Rightarrow \nu_A = 2\nu_B$ $\Rightarrow \frac{1}{2\pi} \sqrt{\frac{M_A}{I}} = 2 \times \frac{1}{2\pi} \sqrt{\frac{M_B}{I}}$ $\Rightarrow M_A = 4M_B$

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
}