Import Question JSON

Current Question (ID: 16821)

Question:

$\text{Two particles each of mass } m \text{ and charge } q \text{ are attached to the two ends of a light rigid rod of length } 2R. \text{ The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. What is the ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod?}$

Options:

1. $\frac{q}{2m}$
2. $\frac{q}{m}$
3. $\frac{2q}{m}$
4. $\frac{q}{\pi m}$

Solution:

$\text{(a) } i = \frac{2q\omega}{2\pi} = \frac{q\omega}{\pi} \Rightarrow M = iA = \frac{q\omega}{\pi} \pi R^2 = q\omega R^2$ $L = 2R \cdot mv = 2R \cdot mR\omega = 2mR^2\omega \; (\because \; v = R\omega)$ $\Rightarrow \frac{M}{L} = \frac{q}{2m}$

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
}