Import Question JSON

Current Question (ID: 19512)

Question:

$\text{On a planet } \rho \text{ (mass density) is same as that of earth while mass of planet is twice than that of earth. Ratio of weight of a body on surface of planet to that on earth is equal to:}$ $1.\ 1$ $2.\ (2)^{1/3}$ $3.\ (2)^{-1/3}$ $4.\ 2$

Options:

1. $1$
2. $(2)^{1/3}$
3. $(2)^{-1/3}$
4. $2$

Solution:

$\text{Hint: } g = \frac{GM}{R^2}$ $\frac{g_p}{g_e} = \frac{GM_p/R_p^2}{GMe/R_e^2} = \left(\frac{M_p/\rho_p^2}{M_e/\rho_e^2}\right)^{1/3}$ $= \left(\frac{M_p}{M_e}\right)^{1/3}$ $= (2)^{1/3}$

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
}