Import Question JSON

Current Question (ID: 10540)

Question:

$\text{The energy needed to break a drop of radius } R \text{ into } n \text{ drops of radii } r \text{ is given by:}$

Options:

1. $4\pi T(nr^2 - R^2)$
2. $\frac{4}{3}\pi(r^3n - R^2)$
3. $4\pi T(R^2 - nr^2)$
4. $4\pi T(nr^2 + R^2)$

Solution:

\text{(a) Energy needed = Increment in surface energy} \text{= (surface energy of n small drops) - (surface energy of one big drop)} \text{= } n \cdot 4\pi r^2 T - 4\pi R^2 T = 4\pi T(nr^2 - R^2)

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
}