Import Question JSON

Current Question (ID: 19517)

Question:

$\text{If the time period for one revolution by satellite near the Earth's surface is } T, \text{ then, the time period of revolution of the satellite at a height equal to the radius of the Earth will be:}$

Options:

1. $\sqrt{8} \, T$
2. $\sqrt{2} \, T$
3. $\sqrt{4} \, T$
4. $\sqrt{3} \, T$

Solution:

$\text{Hint: } T^2 \propto r^3$ $\text{Step: Find the time period of the satellite.}$ $\text{According to Kepler's third law; the square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit}$ $i.e., \ T^2 \propto r^3$ $\Rightarrow \left( \frac{T}{T'} \right)^2 = \left( \frac{R}{2R} \right)^3$ $\Rightarrow T' = \sqrt{8}T$ $\text{Hence, option (1) is the correct answer.}$

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
}