Import Question JSON

Current Question (ID: 19901)

Question:

$\text{A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period } T_1 \text{ and, (ii) back and forth in a direction perpendicular to its plane, with a period } T_2. \text{ The ratio } \frac{T_1}{T_2} \text{ will be:}$

Options:

1. $\frac{2}{\sqrt{3}}$
2. $\sqrt{\frac{2}{3}}$
3. $\frac{2}{3}$
4. $\frac{3}{\sqrt{2}}$

Solution:

$\text{Hint: } T = 2\pi \sqrt{\frac{I}{Mgd}}$ $\text{Moment of inertia in case (i) is } I_1$ $\text{Moment of inertia in case (ii) is } I_2$ $I_1 = 2MR^2$ $I_2 = \frac{3}{2}MR^2$ $T_1 = 2\pi \sqrt{\frac{I_1}{Mgd}}$ $T_2 = 2\pi \sqrt{\frac{I_2}{Mgd}}$ $\frac{T_1}{T_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{2MR^2}{\frac{3}{2}MR^2}} = \frac{2}{\sqrt{3}}$

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
}