Import Question JSON

Current Question (ID: 16941)

Question:

$\text{A circular disc of the radius } 0.2 \text{ m is placed in a uniform magnetic field of induction } \frac{1}{\pi} \left( \frac{\text{Wb}}{\text{m}^2} \right) \text{ in such a way that its axis makes an angle of } 60^\circ \text{ with } \vec{B}. \text{ The magnetic flux linked to the disc will be:}$

Options:

1. $0.02 \text{ Wb}$
2. $0.06 \text{ Wb}$
3. $0.08 \text{ Wb}$
4. $0.01 \text{ Wb}$

Solution:

$\phi = BA \cos \theta$ $\text{Here, } \theta = 60^\circ, B = \frac{1}{\pi} \left( \frac{\text{Wb}}{\text{m}^2} \right), \phi = BA \cos \theta$ $\text{Substitute the known values we get;} \phi = \frac{1}{\pi} \times \pi \times (0.2)^2 \times \cos 60^\circ$ $\phi = (0.2)^2 \times \frac{1}{2}$ $\Rightarrow \phi = 0.02 \text{ Wb}$ $\text{Hence, option (1) is the correct answer.}$

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
}