Import Question JSON

Current Question (ID: 19427)

Question:

$\text{A uniform solid sphere is rolling without slipping on a horizontal surface.}$ $\text{The ratio of translational kinetic energy to the total kinetic energy is } \frac{5}{x}. \text{ Find the value of } x.$

Options:

1. $2$
2. $3$
3. $5$
4. $7$

Solution:

$\frac{K.E._{\text{Trans}}}{K.E._{\text{Total}}} = \frac{\frac{1}{2} m R^2 \omega^2}{\frac{1}{2} \left( \frac{2}{5} + 1 \right) m R^2 \omega^2} = \frac{5}{7}$

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
}