Import Question JSON

Current Question (ID: 19381)

Question:

$\text{A solid sphere is rolling on a smooth surface with kinetic energy equal to } 7 \times 10^{-3} \text{ J. If the mass of the sphere is 1 kg, then the speed of the centre of mass is: (Consider pure rolling)}$

Options:

1. $10 \text{ m/s}$
2. $10 \text{ cm/s}$
3. $20 \text{ m/s}$
4. $20 \text{ cm/s}$

Solution:

$KE = \frac{1}{2} m V_{cm}^2 + \frac{1}{2} I_{cm} \omega^2$ $\text{For pure rolling,}$ $KE = \frac{1}{2} m V_{cm}^2 + \frac{2}{5} m R^2 \left( \frac{V_{cm}}{R} \right)^2$ $7 \times 10^{-3} = \frac{7}{10} m V_{cm}^2$ $V_{cm} = \sqrt{10^{-2}} = 10^{-1} \text{ m/s} = 10 \text{ cm/s}$

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
}