Import Question JSON

Current Question (ID: 20476)

Question:

$\text{Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of } 3 \text{ s and } 4 \text{ s respectively. If their moments of inertia are in the ratio of } 3 : 2 \text{ then the ratio of their magnetic moments will be:}$

Options:

1. $2 : 1$
2. $8 : 3$
3. $1 : 3$
4. $27 : 16$

Solution:

$T = 2\pi \sqrt{\frac{I}{m}}$ $\frac{T_1}{T_2} = \sqrt{\frac{I_1}{I_2} \cdot \frac{m_2}{m_1}}$ $\frac{3}{4} = \sqrt{\frac{3}{2} \cdot \frac{m_2}{m_1}}$ $\left(\frac{3}{4}\right)^2 = \frac{3}{2} \cdot \frac{m_2}{m_1}$ $\frac{m_2}{m_1} = \frac{8}{3}$

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
}