Import Question JSON

Current Question (ID: 19506)

Question:

$\text{An object of mass } 1 \text{ kg is taken to a height from the surface of the Earth which is equal to three times the Earth's radius. The gain in potential energy of the object will be:}$ $\text{(Given: } g = 10 \text{ ms}^{-2} \text{ and radius of Earth } = 6400 \text{ km)}$

Options:

1. $48 \text{ MJ}$
2. $24 \text{ MJ}$
3. $36 \text{ MJ}$
4. $12 \text{ MJ}$

Solution:

$\text{Hint: } P. E = -\frac{GmM}{R}$ $\text{Step: Find the gain in potential energy of the object.}$ $\Delta U = -GMm\left(\frac{1}{r_2} - \frac{1}{r_1}\right)$ $= -mgR^2\left(\frac{1}{4R} - \frac{1}{R}\right)$ $= \frac{3}{4}mgR$ $= 48 \text{ MJ}$ $\text{Hence, option (1) is the correct answer.}$

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
}