Import Question JSON

Current Question (ID: 19476)

Question:

$\text{Given below are two statements:}$ $\text{Statement I: If total energy of a satellite revolving around earth in circular path is } E, \text{ then potential energy of satellite is } 2E.$ $\text{Statement II: Kinetic energy is also twice of total energy.}$

Options:

1. $\text{Statement I is incorrect and Statement II is correct.}$
2. $\text{Both Statement I and Statement II are correct.}$
3. $\text{Both Statement I and Statement II are incorrect.}$
4. $\text{Statement I is correct and Statement II is incorrect.}$

Solution:

$\text{Hint: T. E. = } -\frac{Gm_1m_2}{2r}$ $\text{Explanation:}$ $\text{Total energy } = -\frac{Gm_1m_2}{2r}$ $\text{P. E. } = -\frac{Gm_1m_2}{r}$ $\text{K. E. } = \frac{Gm_1m_2}{2r}$ $\text{So, P. E. = 2E}$ $\text{K. E. = -E}$

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
}