Import Question JSON

Current Question (ID: 10502)

Question:

$\text{A soap bubble, having a radius of 1 mm, is blown from a detergent solution having a surface tension of } 2.5 \times 10^{-2} \text{ N/m. The pressure inside the bubble equals at a point } Z_0 \text{ below the free surface of the water in a container. Taking } g = 10 \text{ m/s}^2, \text{ the density of water } = 10^3 \text{ kg/m}^3, \text{ the value of } Z_0 \text{ is:}$

Options:

1. $0.5 \text{ cm}$
2. $100 \text{ cm}$
3. $10 \text{ cm}$
4. $1 \text{ cm}$

Solution:

\text{A soap bubble has two surfaces. So excess pressure inside the soap bubble } = \frac{4S}{r} S = 2.5 \times 10^{-2} \text{ N/m} \Delta P = \rho g Z_0 \frac{4S}{r} = g \rho Z_0 \frac{4 \times 2.5 \times 10^{-2}}{10^{-3}} = 10 \times 10^3 \times Z_0 Z_0 = \frac{10 \times 10^{-2} \times 10^3}{10 \times 10^3} Z_0 = 0.01 \text{ m} Z_0 = 1 \text{ cm}

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
}