Import Question JSON

Current Question (ID: 19600)

Question:

$\text{A liquid drop of radius } R \text{ is divided into } 27 \text{ identical drops. If the surface tension of the drops is } T, \text{ then the work done in this process is:}$

Options:

1. $4\pi R^2 T$
2. $3\pi R^2 T$
3. $8\pi R^2 T$
4. $\frac{1}{8} \pi R^2 T$

Solution:

$\text{Hint: } W = T \times \Delta S$ $W = T \times \text{change in area } (\Delta S)$ $\text{From volume conservation}$ $\frac{4}{3} \pi R^3 = 27 \pi r^3 \times \frac{4}{3}$ $R = 3r$ $r = \frac{R}{3}$ $\therefore \Delta S = 4\pi r^2 \times 27 - 4\pi R^2$ $= 4\pi \times \frac{R^2}{9} \times 27 - 4\pi R^2 = 2 \left(4\pi R^2\right)$ $W = 8\pi R^2 T$

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
}