Import Question JSON

Current Question (ID: 19484)

Question:

$\text{A very long (length } L) \text{ cylindrical galaxy is made of uniformly}$ $\text{distributed mass and has radius } R (R \gg L). \text{ A star outside the}$ $\text{galaxy is orbiting the galaxy in a plane perpendicular to the galaxy}$ $\text{and passing through its centre. If the time period of the star is } T \text{ and}$ $\text{its distance from the galaxy's axis is } r, \text{ then:}$

Options:

1. $T \propto r$
2. $T \propto \sqrt{r}$
3. $T \propto r^2$
4. $T^2 \propto r^3$

Solution:

$\text{Hint: Use the concept of Newton's law of gravitation.}$

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
}