Import Question JSON

Current Question (ID: 19515)

Question:

$\text{An object weighs } 200 \ N \text{ at the surface of earth. Find the weight at a depth of } \frac{R}{2}, \text{ where } R \text{ is the radius of earth.}$

Options:

1. $100 \ N$
2. $300 \ N$
3. $50 \ N$
4. $150 \ N$

Solution:

$\text{Hint: } g' = g \left(1 - \frac{d}{R}\right)$ $g' = g \left[1 - \frac{d}{R}\right]$ $= g \left[1 - \frac{R/2}{R}\right]$ $= \frac{g}{2}$ $\Rightarrow W' = \frac{W}{2} = 100 \ N.$

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
}