Import Question JSON

Current Question (ID: 10513)

Question:

$\text{In a capillary tube experiment, a vertical 30 cm long capillary tube is dipped in water. The water rises up to a height of 10 cm due to capillary action. If this experiment is conducted in a freely falling elevator, the length of the water column becomes:}$

Options:

1. $\text{10 cm}$
2. $\text{20 cm}$
3. $\text{30 cm}$
4. $\text{Zero}$

Solution:

\text{From Newton's first law of motion:} F_{\text{cap}} = W \text{where } W \text{ is the weight of water column and } F_{\text{cap}} \text{ is the capillary force} \text{Weight of water column: } W = mg = \rho h S g \text{Variables:} \rho \text{ - density of water} g \text{ - acceleration due to gravity} h \text{ - height of column} S \text{ - cross-sectional area of tube} \text{In freely falling elevator: } W = 0 \text{Since capillary force is constant, water fills entire tube: } h = 30 \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
}