Import Question JSON

Current Question (ID: 19380)

Question:

$\text{A disc of radius } R \text{ is given by } \omega_0 \text{ angular speed and placed gently on a rough horizontal surface.}$ $\text{What is the velocity of center of the disc when pure rolling starts?}$

Options:

1. $\frac{R\omega_0}{3}$
2. $R\omega_0$
3. $\frac{R\omega_0}{4}$
4. $2R\omega_0$

Solution:

$\text{Hint: Conserve the angular momentum.}$ $I_{CM}\omega_0 = \left(I_{CM} + MR^2\right) \omega$ $\frac{1}{2} MR^2 \omega_0 = \frac{3}{2} MR^2 \omega$ $\omega_0 = 3\omega$ $\Rightarrow \left(v_{cm}\right)_f = R\omega = \frac{R\omega_0}{3}$

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
}