Import Question JSON

Current Question (ID: 19574)

Question:

$\text{When a long glass capillary tube of radius } 0.015 \text{ cm is dipped in a liquid, the liquid rises to a height of } 15 \text{ cm within it.}$ $\text{If the contact angle between the liquid and glass to close to } 0^\circ, \text{ the surface tension of the liquid, in milliNewton m}^{-1}, \text{ is:}$ $\left[ \rho(\text{liquid}) = 900 \text{ kgm}^{-3}, \ g = 10 \text{ ms}^{-2} \right] \text{ (Give answer in closest integer).}$

Options:

1. $200$
2. $101$
3. $402$
4. $325$

Solution:

$\text{Hint: } h = \frac{2S \cos \theta}{\rho rg}$ $\text{Ans is } 101$ $\text{Capillary rise}$ $h = \frac{2S \cos \theta}{\rho gr}$ $S = \frac{(900) \times (10) \times (15 \times 10^{-2})}{2}$ $S = 1012.5 \times 10^{-4}$ $S = 101.25 \times 10^{-3} = 101.25 \text{ N/m}$ $\text{In question closest integer is asked so closest integer } = 101.00 \text{ Ans.}$

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
}