Import Question JSON

Current Question (ID: 10539)

Question:

$\text{If the excess pressure inside a soap bubble is balanced by an oil column of height of 2 mm, then the surface tension of the soap solution will be:}$ $\text{(the radius of the soap bubble, } r = 1 \text{ cm and density of oil, } d = 0.8 \text{ gm/cm}^3\text{)}$

Options:

1. $3.9 \text{ N/m}$
2. $3.9 \times 10^{-2} \text{ N/m}$
3. $3.9 \times 10^{-3} \text{ N/m}$
4. $3.9 \text{ dyne/m}$

Solution:

\text{For a soap bubble, the excess pressure formula is: } \frac{4T}{R} = \rho g h \text{Therefore: } T = \frac{R \rho g h}{4} \text{Substituting the values:} T = \frac{10^{-2} \times 2 \times 10^{-3} \times 0.8 \times 10^3 \times 9.8}{4} = 3.9 \times 10^{-2} \text{ N/m}

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
}