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Current Question (ID: 10498)

Question:

$\text{A rectangular film of liquid is extended from (4 cm × 2 cm) to (5 cm × 4 cm). If the work done is } 3 \times 10^{-4} \text{ J, the value of the surface tension of the liquid is:}$

Options:

1. $0.25 \text{ N/m}$
2. $0.125 \text{ N/m}$
3. $0.2 \text{ N/m}$
4. $8.0 \text{ N/m}$

Solution:

$\text{(b) Increase in surface energy = increase in area × Surface tension}$ $\text{∴ Increase in surface area,}$ $\Delta A = (5 \times 4 - 4 \times 2) \times 2 \quad (\because \text{film has two surfaces})$ $= (20 - 8) \times 2 \text{ cm}^2 = 24 \text{ cm}^2 = 24 \times 10^{-4} \text{ m}^2$ $\text{So, work done, } W = T \cdot \Delta A$ $3 \times 10^{-4} = T \times 24 \times 10^{-4}$ $\therefore T = \frac{1}{8} = 0.125 \text{ N/m}$ $\text{A film has two sides and the liquid in between}$

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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
}