Import Question JSON

Current Question (ID: 19516)

Question:

$\text{The mass and radius of orbit for the two satellites are } (m, r) \text{ and } (3m, 3r) \text{ respectively. What will be the ratio of their orbital velocity about the Earth?}$

Options:

1. $\sqrt{3} : 1$
2. $1 : \sqrt{3}$
3. $\sqrt{2} : 1$
4. $1 : 2$

Solution:

$\text{Hint: } v = \sqrt{\frac{GM}{r}}$ $\text{Step: Find the ratio of orbital velocities.}$ $v_1 = \sqrt{\frac{GM}{r}}, \quad v_2 = \sqrt{\frac{GM}{3r}}$ $\therefore \frac{v_1}{v_2} = \frac{\sqrt{3}}{1}$ $\text{Hence, option (1) is the correct answer.}$

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
}