Import Question JSON

Current Question (ID: 10133)

Question:

$\text{The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:}$

Options:

1. $\text{B}$
2. $\text{C}$
3. $\text{D}$
4. $\text{A}$

Solution:

$\text{Moment of inertia of circular disc} = \frac{1}{2}mR^2$ $\text{Thus, as the distance between the center and the point increases, moment of inertia increases.}$ $\text{From the diagram, point B is at the edge of the disc and is farthest from the center, making it the point where the moment of inertia would be maximum when the axis passes through it perpendicular to the disc.}$

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
}