Import Question JSON

Current Question (ID: 19321)

Question:

$\text{From a uniform circular disc of radius } R \text{ and mass } 9M, \text{ a small disc of radius } \frac{R}{3} \text{ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of the disc is:}$

Options:

1. $4MR^2$
2. $\frac{40}{9}MR^2$
3. $10MR^2$
4. $\frac{37}{9}MR^2$

Solution:

$\text{Hint: } I_{\text{at centre}} = I_{\text{big disc}} - I_{\text{small disc}}$ $I_{\text{at centre}} = I_{\text{big disc}} - I_{\text{small disc}}$ $= \frac{9MR^2}{2} - \left[ M \left( \frac{R}{3} \right)^2 \frac{1}{2} + M \left( \frac{2R}{3} \right)^2 \right]$ $= \frac{9MR^2}{2} - \left[ \frac{MR^2}{18} + M \times \frac{4R^2}{9} \right]$ $= \frac{9MR^2}{2} - \frac{MR^2}{2}$ $= 4MR^2$

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
}