Import Question JSON

Current Question (ID: 19528)

Question:

$\text{A satellite of } 103 \text{ kg mass is revolving in circular orbit of radius } 2R. \text{ If } \frac{10^4R}{6} \text{ J energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use } g = 10 \text{ m/s}^2, R = \text{ radius of earth})$

Options:

1. $2.5 R$
2. $6 R$
3. $3 R$
4. $4 R$

Solution:

$\text{The energy supplied to the satellite is used to increase its potential energy.}$ $\text{The potential energy of a satellite in orbit of radius } r \text{ is given by } U = -\frac{GMm}{r}.$ $\text{The change in potential energy } \Delta U = U_{\text{final}} - U_{\text{initial}} = \frac{GMm}{r_{\text{final}}} - \frac{GMm}{r_{\text{initial}}}.$ $\text{Given } \Delta U = \frac{10^4R}{6}, \text{ solve for } r_{\text{final}}.$

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
}