Import Question JSON

Current Question (ID: 19447)

Question:

$\text{A satellite is in an elliptical orbit around a planet } P. \text{ It is observed that the velocity of the satellite when it is farthest from the planet is } 6 \text{ times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:}$

Options:

1. $1 : 3$
2. $1 : 2$
3. $3 : 4$
4. $1 : 6$

Solution:

$\text{Hint: Angular momentum is conserved.}$ $\text{By angular momentum conservation}$ $r_{\min} v_{\max} = r_{\max} v_{\min}$ $\text{Given } v_{\min} = \frac{v_{\max}}{6}$ $\text{From equation (i)}$ \frac{r_{\min}}{r_{\max}} = \frac{v_{\min}}{v_{\max}} = \frac{1}{6}$

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
}