Import Question JSON

Current Question (ID: 10545)

Question:

$\text{If the surface tension of water is } 0.06 \text{ N/m}^2, \text{ then the capillary rise in a tube of diameter 1 mm is:}$ $(\theta = 0°)$

Options:

1. $1.22 \text{ m}$
2. $2.44 \text{ cm}$
3. $3.12 \text{ cm}$
4. $3.86 \text{ cm}$

Solution:

\text{Given: Surface tension } T = 0.06 \text{ N/m, diameter } = 1 \text{ mm, so radius } r = 0.5 \text{ mm} = 5 \times 10^{-4} \text{ m, } \theta = 0° \text{Using the formula for capillary rise: } h = \frac{2T \cos \theta}{r\rho g} h = \frac{2 \times 0.06 \times \cos(0°)}{5 \times 10^{-4} \times 10^3 \times 10} = \frac{2 \times 6 \times 10^{-2} \times 1}{5 \times 10^{-4} \times 10^3 \times 10} = 2.4 \times 10^{-2} \text{ m} = 2.4 \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
}