Import Question JSON

Current Question (ID: 19477)

Question:

$\text{A planet has a mass equal to 16 times the mass of Earth, and a radius equal to 4 times that of Earth. The ratio of the escape speed of the planet to that of Earth will be:}$

Options:

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

Solution:

$\text{Hint: } v_e = \sqrt{\frac{2GM}{r}}$ $\text{Step: Find the ratio of the escape speed of the planet to that of the earth.}$ $v = \sqrt{\frac{2GM}{R}}$ $\frac{v_p}{v_e} = \sqrt{\frac{2GM_p}{R_p}} \times \sqrt{\frac{R_e}{2GM_e}}$ $= \sqrt{\frac{16}{4}} = 2$ $\text{Hence, option (1) is the correct answer.}$

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
}