Import Question JSON

Current Question (ID: 19409)

Question:

$\text{The moment of inertia of an equilateral triangular lamina } ABC, \text{ about the axis passing through its centre } O \text{ and perpendicular to its plane is } I_0 \text{ as shown in the figure.}$ $\text{A cavity } DEF \text{ is cut out from the lamina, where } D, E, F \text{ are the midpoints of the sides.}$ $\text{The moment of inertia of the remaining part of the lamina about the same axis is:}$

Options:

1. $\frac{31}{32} I_0$
2. $\frac{3}{4} I_0$
3. $\frac{7}{8} I_0$
4. $\frac{15}{16} I_0$

Solution:

$\text{Hint: } I = \sum m_i r_i^2$

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
}