Import Question JSON

Current Question (ID: 19473)

Question:

$\text{If mass of a planet is 9 times that of the earth and radius is 2 times that of the earth, then the escape speed from this planet is:}$ $\left(v_e \text{ is escape speed from the Earth.}\right)$

Options:

1. $\frac{v_e}{\sqrt{2}}$
2. $\frac{v_e}{2\sqrt{2}}$
3. $\frac{3v_e}{\sqrt{2}}$
4. $\frac{v_e}{2}$

Solution:

$\text{Hint: Use } v_e = \sqrt{\frac{2GM}{R_e}}$ $\text{Step: Calculate the escape velocity of the earth and planet.}$ $\text{Escape speed from the Earth, } v_e = \sqrt{\frac{2GM_e}{R_e}}$ $\text{Escape speed from the planet, } v_p = \sqrt{\frac{2GM'}{R'}} = \sqrt{\frac{2G \times 9M_e}{2R_e}} = v_e \times \frac{3}{\sqrt{2}}$ $\Rightarrow v_p = \frac{3v_e}{\sqrt{2}}$

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
}