Import Question JSON

Current Question (ID: 19421)

Question:

$\text{A disc of mass } 1 \text{ kg and radius } R \text{ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of the disc. A body of the same mass as that of the disc is fixed at the highest point of the disc. Now the system is released. When the body comes to the lowest position, its angular speed will be: (take } g = 10 \text{ ms}^{-2})$

Options:

1. $4 \sqrt{\frac{5}{3R}} \text{ rad/s}$
2. $4 \sqrt{\frac{4}{3R}} \text{ rad/s}$
3. $4 \sqrt{\frac{1}{R}} \text{ rad/s}$
4. $4 \sqrt{\frac{1}{3R}} \text{ rad/s}$

Solution:

$\text{Hint: use conservation of mechanical energy.}$

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
}