Import Question JSON

Current Question (ID: 19468)

Question:

$\text{The period of a pendulum at the earth's surface is } T. \text{ The time period of the pendulum at distance (from centre) which is twice the radius of the earth is:}$

Options:

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

Solution:

$\text{We know that:}$ $T = 2\pi \sqrt{\frac{l}{g}}$ $\text{Case 1:}$ $T = 2\pi \sqrt{\frac{l}{GM/R^2}}$ $\text{Case 2:}$ $T' = 2\pi \sqrt{\frac{l}{GM/4R^2}}$ $\text{So,}$ \frac{T'}{T} = \frac{2}{1} \Rightarrow T' = 2T$

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
}