Import Question JSON

Current Question (ID: 10266)

Question:

$\text{From a circular ring of mass } M \text{ and radius } R\text{, an arc corresponding to a } 90^\circ \text{ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is } K \text{ times } MR^2\text{. The value of } K \text{ will be:}$

Options:

1. $\frac{1}{4}$
2. $\frac{1}{8}$
3. $\frac{3}{4}$
4. $\frac{7}{8}$

Solution:

\text{Hint: Subtract MOI of the removed part from the complete ring.} \\[0.5em] \text{Step 1: Find the MOI of the complete ring.} \\[0.5em] \text{MOI of the complete ring, } I_1 = MR^2 \\[0.5em] \text{Step 2: Find the MOI of the removed part.} \\[0.5em] \text{MOI of the removed part, } I_2 = \frac{1}{4} \cdot MR^2 \\[0.5em] \text{Step 3: Find the MOI of the remaining part.} \\[0.5em] \text{MOI of the remaining part } = I_1 - I_2 = \frac{3}{4}MR^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
}