Import Question JSON

Current Question (ID: 20410)

Question:

$\text{A galvanometer coil has } 500 \text{ turns and each turn has an average area of } 3 \times 10^{-4} \text{ m}^2. \text{ If a torque of } 1.5 \text{ Nm is required to keep this coil parallel to a magnetic field when a current of } 0.5 \text{ A is flowing through it, the strength of the field (in T) is:}$ $1. \ 10$ $2. \ 40$ $3. \ 20$ $4. \ 30$

Options:

1. $10$
2. $40$
3. $20$
4. $30$

Solution:

$\text{Hint: } \vec{\tau} = \vec{m} \times \vec{B}.$ $\text{Ans is } 20$ $\vec{T} = \vec{m} \times \vec{B}$ $T = NI \times A \times B$ $1.5 = 500 \times 0.5 \times 3 \times 10^{-4} \times B$ $B = 20$

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
}