Import Question JSON

Current Question (ID: 20481)

Question:

$\text{The magnetic moment of a bar magnet is } 0.5 \text{ Am}^2. \text{ It is suspended in a uniform magnetic field of } 8 \times 10^{-2} \text{ T. The work done in rotating it from its most stable to most unstable position is } -$ $1. \ 16 \times 10^{-2} \text{ J}$ $2. \ \text{zero}$ $3. \ 8 \times 10^{-2} \text{ J}$ $4. \ 4 \times 10^{-2} \text{ J}$

Options:

1. $16 \times 10^{-2} \text{ J}$
2. $\text{zero}$
3. $8 \times 10^{-2} \text{ J}$
4. $4 \times 10^{-2} \text{ J}$

Solution:

$\text{Hint: } U = -MB \cos \theta$ $\text{Step: Find the work done in rotating bar magnet from its most stable to most unstable position.}$ $W = \Delta U$ $\Rightarrow W = U_f - U_i$ $\Rightarrow W = (-MB \cos 180^\circ) - (-MB \cos 0^\circ)$ $\Rightarrow W = 2MB$ $\Rightarrow W = 2 \times \frac{1}{2} \times 8 \times 10^{-2}$ $\Rightarrow W = 8 \times 10^{-2} \text{ J}$ $\text{Hence, option (3) is the correct answer.}$

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
}