Import Question JSON

Current Question (ID: 10209)

Question:

$\text{A circular disc is to be made by using iron and aluminium so that it acquires a maximum moment of inertia about its geometrical axis. It is possible with:}$

Options:

1. $\text{Aluminium in the interior and iron surrounding it}$
2. $\text{Iron at the interior and aluminium surrounding it}$
3. $\text{Using iron and aluminium layers in alternate order}$
4. $\text{A sheet of iron is used at both the external surface and aluminium sheet as the internal layer}$

Solution:

$\text{To maximize the moment of inertia of a circular disc, the material with higher density should be placed as far as possible from the axis of rotation.}$ $\text{Iron is denser than aluminium. Therefore, to achieve a maximum moment of inertia, iron should be placed in the outer regions and aluminium in the interior.}$ $\text{The correct option is: 1. Aluminium in the interior and iron surrounding it}$

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
}