Import Question JSON

Current Question (ID: 10328)

Question:

$\text{The moment of inertia of a thin uniform circular disc about one of its diameter is I. Its moment of inertia about an axis perpendicular to the circular surface and passing through its center will be:}$

Options:

1. $\sqrt{2I}$
2. $2I$
3. $\frac{I}{2}$
4. $\frac{I}{\sqrt{2}}$

Solution:

$\text{Moment of inertia of thin uniform circular disc about one of its diameter is } I$ $\therefore I = \frac{MR^2}{4} \ldots (i)$ $\text{where M is the mass and R is the radius of the disc. Moment of inertia of disc about an axis passing through the centre and perpendicular to the plane of the disc is } I'$ $I' = \frac{MR^2}{2} = 2\left(\frac{MR^2}{4}\right) = 2I \text{ [Using } (i)\text{]}$

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
}