Import Question JSON

Current Question (ID: 16871)

Question:

$\text{A bar magnet of length } l \text{ and magnetic dipole moment } M \text{ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be:}$

Options:

1. $\frac{3M}{\pi}$
2. $\frac{2M}{l\pi}$
3. $\frac{M}{2}$
4. $M$

Solution:

$\text{Hint: The dipole moment depends on the effective length between the poles.}$ $\text{Step 1: Find the initial dipole moment.}$ $\text{Let the magnetic dipole strength be } m, \text{ then,}$ $M = ml$ $\text{Step 2: Find the final dipole moment.}$ $\text{As stated in the question, we get,}$ $M' = (m)\{2r\sin(60^\circ/2)\}$ $M' = 2m\left(\frac{3l}{\pi}\right)\left(\frac{1}{2}\right) = \frac{3ml}{\pi} = \frac{3M}{\pi}$ $\text{Hence, the correct answer is option A.}$

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
}