Import Question JSON

Current Question (ID: 9858)

Question:

$\text{A uniform chain of length } L \text{ and mass } M \text{ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If } g \text{ is acceleration due to gravity, the work required to pull the hanging part on the table is:}$

Options:

1. $MgL$
2. $\frac{MgL}{3}$
3. $\frac{MgL}{9}$
4. $\frac{MgL}{18}$

Solution:

$\text{Work done = potential energy of the hanging chain}$ $= mgh$ $= \frac{M}{L} \times \frac{L}{3} \times g \times \frac{1}{2} \left(\frac{L}{3}\right) = \frac{MgL}{18}$

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
}