Import Question JSON

Current Question (ID: 19369)

Question:

$\text{A spherical shell of } 1 \text{ kg mass and radius } R \text{ is rolling with angular speed } \omega \text{ on a horizontal plane (as shown in the figure). The magnitude of angular momentum of the shell about the origin } O \text{ is } \frac{a}{3} R^2 \omega. \text{ The value of } a \text{ will be:}$

Options:

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

Solution:

$\text{Hint: } L_0 = (mv_{cm}r + I\omega)$ $\text{Step: Find the value of } a.$ $L = Mv_{cm}R + I_{cm}\omega$ $= M(\omega R)R + \frac{2}{3} MR^2 \omega$ $L = \frac{5}{3} MR^2 \omega = \frac{a}{3} R^2 \omega$ $\Rightarrow a = 5$

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
}