Import Question JSON

Current Question (ID: 19405)

Question:

$\text{A particle of mass } 2 \text{ kg is on a smooth horizontal table and moves in a circular path of radius } 0.6 \text{ m.}$ $\text{The height of the table from the ground is } 0.8 \text{ m.}$ $\text{If the angular speed of the particle is } 12 \text{ rad s}^{-1},$ $\text{the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:}$

Options:

1. $14.4 \text{ kg m}^2\text{s}^{-1}$
2. $8.64 \text{ kg m}^2\text{s}^{-1}$
3. $20.16 \text{ kg m}^2\text{s}^{-1}$
4. $11.52 \text{ kg m}^2\text{s}^{-1}$

Solution:

$\text{Hint: } L = mvr$

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
}