Import Question JSON

Current Question (ID: 19488)

Question:

$\text{Take the mean distance of the moon and the sun from the earth to be } 0.4 \times 10^6 \text{ km and } 150 \times 10^6 \text{ km respectively. Their masses are } 8 \times 10^{22} \text{ kg and } 2 \times 10^{30} \text{ kg respectively. The radius of the earth is } 6400 \text{ km. Let } \Delta F_1 \text{ be the difference in the forces exerted by the moon at the nearest and farthest point on the earth and } \Delta F_2 \text{ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to } \frac{\Delta F_1}{\Delta F_2} \text{ is:}$

Options:

1. $6$
2. $10^{-2}$
3. $2$
4. $0.6$

Solution:

$\text{Hint: } F = \frac{Gm_1m_2}{r^2}$

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
}