Import Question JSON

Current Question (ID: 20528)

Question:

$\text{A metal rod of length } 1 \text{ m is moving perpendicular to its length with } 8 \text{ m/s velocity along the positive } x\text{-axis. A magnetic field } B = 2 \text{ T exists perpendicular to the plane of motion. The EMF induced between the two ends of the rod is:}$ $1. \ 16 \text{ V}$ $2. \ 0 \text{ V}$ $3. \ 8 \text{ V}$ $4. \ 4 \text{ V}$

Options:

1. $16 \text{ V}$
2. $0 \text{ V}$
3. $8 \text{ V}$
4. $4 \text{ V}$

Solution:

$\text{Hint: } \varepsilon = Bvl$ $\text{Step: Find the emf induced between the two ends of the rod.}$ $\text{The emf induced between the two ends of the rod is given by;}$ $|\varepsilon| = Bvl$ $\Rightarrow |\varepsilon| = 2 \times 8 \times 1 = 16 \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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
}