Import Question JSON

Current Question (ID: 19387)

Question:

$\text{The moment of inertia of a semi-circular ring of mass } M \text{ and radius } R \text{ about an axis passing through the centre and perpendicular to the plane of the ring is:}$

Options:

1. $MR^2$
2. $\frac{1}{2}MR^2$
3. $2MR^2$
4. $\frac{3}{4}MR^2$

Solution:

$\text{Hint: The moment of inertia of the entire ring } I = 2MR^2$ $\text{Step: Find the moment of inertia of a semi-circular ring.}$ $\text{The distance of the mass from the centre is the same.}$ $\text{Therefore, the moment of inertia is given by;}$ $\Rightarrow I = \int dmR^2$ $\Rightarrow I = R^2 \int dm = MR^2$ $\text{Hence, option (1) is the correct answer.}$

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
}