Import Question JSON

Current Question (ID: 19589)

Question:

$\text{A big drop is divided into 1000 identical droplets. If the big drop had surface energy } U_i \text{ and all small droplets together had a surface energy } U_f, \text{ then } \frac{U_i}{U_f} \text{ is equal to:}$

Options:

1. $\frac{1}{100}$
2. $10$
3. $\frac{1}{10}$
4. $1000$

Solution:

$\text{Volume will remain constant in the process.}$ $\frac{4}{3} \pi R^3 = 1000 \times \frac{4}{3} \pi r^3 \Rightarrow R = 10r$ $\text{Surface energy of big drop}$ $U_i = 4 \pi R^2 T$ $\text{Surface energy of all the small drops,}$ $U_f = 1000 \times 4 \pi r^2 T = 40 \pi R^2 T$ $\text{Taking the ratio, we get,}$ $\frac{U_i}{U_f} = \frac{4 \pi R^2 T}{40 \pi R^2 T} = \frac{1}{10}$

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
}