Import Question JSON

Current Question (ID: 10492)

Question:

$\text{If a small drop of water falls from rest through a large height } h \text{ in air, then the final velocity is:}$

Options:

1. $\propto \sqrt{h}$
2. $\propto h$
3. $\propto (1/h)$
4. $\text{Almost independent of } h$

Solution:

$\text{When a small drop of water falls through a large height in the air, it experiences air resistance. As the velocity increases, the air resistance also increases. Eventually, the air resistance will balance the force of gravity, and the drop will reach a constant velocity known as terminal velocity.}$ $\text{Once the drop reaches terminal velocity, its velocity no longer increases with further increases in height. Therefore, for a 'large height,' the final velocity will be the terminal velocity, which is almost independent of the height from which it fell (as long as the height is sufficient for terminal velocity to be reached).}$ $\text{So, the correct answer is: Almost independent of } h.$

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
}