Import Question JSON

Current Question (ID: 10214)

Question:

$\text{The body of mass 1.5 kg rotating about an axis with angular velocity of 0.3 rad s}^{-1} \text{ has the angular momentum of 1.8 kg m}^2\text{s}^{-1}\text{. The radius of gyration of the body about the axis is:}$

Options:

1. $\text{2 m}$
2. $\text{1.2 m}$
3. $\text{0.2 m}$
4. $\text{1.6 m}$

Solution:

$\text{Hint: } L = I\omega$ $\text{Step 1: Find the moment of inertia of the body is given by}$ $L = I\omega I = 6 \text{ kg-m}^2$ $\text{Step 2: Find the radius of gyration of the body about the axis is given by}$ $I = Mk^2$ $6 = 1.5k^2$ $k = 2 \text{ m}$ $\text{Hence, option (1) is the correct answer.}$

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
}