Import Question JSON

Current Question (ID: 10269)

Question:

$\text{Four-point masses each of value } m \text{ are placed at the corners of a square } ABCD \text{ of side } l\text{. The moment of inertia of this system about an axis passing through } A \text{ and parallel to } BD \text{ will be:}$

Options:

1. $2ml^2$
2. $4ml^2$
3. $3ml^2$
4. $ml^2$

Solution:

$I = I_A + I_B + I_C + I_D$ $= 0 + m\left(\frac{l}{2}\right)^2 + m(2l)^2 + m\left(\frac{l}{2}\right)^2 = \frac{ml^2}{2} + 2ml^2 + \frac{ml^2}{2}$ $= 3ml^2$

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
}