Import Question JSON

Current Question (ID: 19525)

Question:

$\text{Assuming the earth to be a sphere of uniform mass density, a body weighed } 300 \text{ N on the surface of earth. How much it would weight at } \frac{R}{4} \text{ depth under surface of earth?}$

Options:

1. $300 \text{ N}$
2. $75 \text{ N}$
3. $225 \text{ N}$
4. $375 \text{ N}$

Solution:

$\text{Weight at depth } d = W \left(1 - \frac{d}{R}\right)$ $\text{Given } W = 300 \text{ N, } d = \frac{R}{4}$ $\text{Weight at } \frac{R}{4} = 300 \left(1 - \frac{1}{4}\right) = 300 \times \frac{3}{4} = 225 \text{ N}$

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
}