Import Question JSON

Current Question (ID: 19344)

Question:

$\text{For a uniform rectangular sheet shown in the figure, if } I_O \text{ and } I_{O'} \text{ be moments of inertia about the axes perpendicular to the sheet and passing through } O \text{ (the centre of mass) and } O' \text{ (corner point), then:}$

Options:

1. $I_{O'} = I_O$
2. $I_{O'} < I_O$
3. $I_{O'} > I_O$
4. $\text{can't say}$

Solution:

$\text{Hint: Use the parallel axis theorem}$ $\text{Step: Compare the moment of inertia } I_O \text{ and } I_{O'}. \text{ The moment of inertia about the axis } O' \text{ is given by:}$ $I'_{O'} = I_O + Md^2$ $\text{where } d \text{ is the distance between the axis passing through } O \text{ and } O'.$ $\text{Therefore, the correct relation between the moment of inertia is } I_{O'} > I_O.$ $\text{Hence, option (3) is the correct answer.}$

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
}