Import Question JSON

Current Question (ID: 10327)

Question:

$\text{Two uniform, thin, identical rods, each of mass } M \text{ and length } l \text{ are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and are perpendicular to the plane of the cross?}$

Options:

1. $\frac{Ml^2}{12}$
2. $\frac{Ml^2}{6}$
3. $\frac{Ml^2}{4}$
4. $\frac{Ml^2}{3}$

Solution:

$I = 4\left[\frac{M}{2} \cdot \frac{(l/2)^2}{3}\right] = \frac{Ml^2}{6}$

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
}