Import Question JSON

Current Question (ID: 16835)

Question:

$\text{A coil in the shape of an equilateral triangle of side } l \text{ is suspended between the pole pieces of a permanent magnet such that } \vec{B} \text{ is in the plane of the coil. If due to a current } i \text{ in the triangle, a torque } \tau \text{ acts on it, the side } l \text{ of the triangle will be:}$

Options:

1. $\frac{2}{\sqrt{3}} \left( \frac{\tau}{Bi} \right)$
2. $\frac{1}{\sqrt{3}} \frac{\tau}{Bi}$
3. $2 \left( \frac{\tau}{\sqrt{3}Bi} \right)^{\frac{1}{2}}$
4. $\frac{2}{\sqrt{3}} \left( \frac{\tau}{Bi} \right)^{\frac{1}{2}}$

Solution:

$\tau = MB = \left( IA \right) B = I \frac{\sqrt{3}}{4} l^2 B \Rightarrow l = 2 \left( \frac{\tau}{\sqrt{3}BI} \right)^{\frac{1}{2}}$

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
}