Import Question JSON

Current Question (ID: 19408)

Question:

$\text{A uniform disc of radius } R \text{ and mass } M \text{ is free to rotate only about its axis.}$ $\text{A string is wrapped over its rim and a body of mass } m \text{ is tied to the free end of the string as shown in the figure.}$ $\text{The body is released from rest. Then the acceleration of the body is:}$

Options:

1. $\frac{2Mg}{2m+M}$
2. $\frac{2m+M}{2Mg}$
3. $\frac{2Mg}{2M+m}$
4. $\frac{2M+m}{2mg}$

Solution:

$\text{Hint: } \tau = I \alpha$

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
}