Import Question JSON

Current Question (ID: 10251)

Question:

$\text{Five particles of mass 2 kg each are attached to the circumference of a circular disc of a radius of 0.1 m and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane will be:}$

Options:

1. $1 \text{ kg-m}^2$
2. $0.1 \text{ kg-m}^2$
3. $2 \text{ kg-m}^2$
4. $0.2 \text{ kg-m}^2$

Solution:

$\text{Hint: } I_{\text{net}} = \sum m_i r_i^2$ $\text{Step 1: Draw a diagram}$ $\text{The diagram shows five particles of mass m each attached to the circumference of a circular disc with center C.}$ $\text{Step 2: Find the moment of inertia about the required axis}$ $I_C = 5 \times m \times r^2$ $= 5 \times 2 \times (0.1)^2 = 0.1 \text{ kg-m}^2$

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
}