Import Question JSON

Current Question (ID: 19590)

Question:

$\text{The amount of work required to expand the soap bubble from a radius of } r_1 = 3.5 \text{ cm to } r_2 = 7.0 \text{ cm is:}$ $\text{(given surface tension of soap solution, } T = 0.03 \text{ N/m)}$

Options:

1. $0.14 \text{ mJ}$
2. $1.4 \text{ mJ}$
3. $0.7 \text{ mJ}$
4. $2.8 \text{ mJ}$

Solution:

$\text{Hint: Work done = Change in surface energy of soap bubble}$ $\text{Step: Find the amount of work required to expand the soap bubble.}$ $\text{The schematic diagram of both the soap bubbles is shown below,}$ $W = 2T \left(4\pi r_2^2 - 4\pi r_1^2\right) = 8\pi T \left(r_2^2 - r_1^2\right)$ $\Rightarrow W = 8 \times 3.14 \times 0.03 \times \left(49 - 12.25\right) \times 10^{-4} \text{ J}$ $\Rightarrow W = 27.69 \times 10^{-4} \text{ J} \approx 2.8 \text{ mJ}$ $\text{Hence, option (4) is the correct answer.}$

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
}