Import Question JSON

Current Question (ID: 19566)

Question:

$\text{If } M \text{ is the mass of water that rises in a capillary tube of radius } r, \text{ then mass of water which will rise in a capillary tube of radius } 2r \text{ is:}$

Options:

1. $M$
2. $4M$
3. $M/2$
4. $2M$

Solution:

$\text{Hint: } h = \frac{2T \cos \theta}{\rho gr}$ $\text{Step: Find the mass of water rising in a capillary tube.}$ $\text{The height of water rise in a capillary tube due to surface tension is given by;} \ h = \frac{2T \cos \theta}{\rho gr}$ $\text{The volume of water that rises in the capillary tube is given by;} \ V = \pi r^2 h$ $\text{Thus, the mass } M \text{ of the water that rises is given by;} \ M = \rho V = \rho \pi r^2 h$ $\text{Substituting } h = \frac{2T \cos \theta}{\rho gr}, \text{ we get:}$ $M = \rho \pi r^2 \times \frac{2T \cos \theta}{\rho gr}$ $M = \frac{2\pi T \cos \theta}{g} r$ $\text{Now, for a capillary tube with a radius } 2r, \text{ and the mass } M' \text{ of water that rises will be:}$ $M' = \frac{2\pi T \cos \theta}{g} (2r)$ $M' = 2M$ $\text{Hence, option (4) is the correct answer.}$

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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
}