Import Question JSON

Current Question (ID: 19060)

Question:

$\text{When a ball is dropped into a lake from a height } 4.9 \text{ m above the water level, it hits the water with a velocity } v \text{ and then sinks to the bottom with the constant velocity } v. \text{ It reaches the bottom of the lake } 4.0 \text{ s after it is dropped. The approximate depth of the lake is:}$

Options:

1. $19.6 \text{ m}$
2. $29.4 \text{ m}$
3. $39.2 \text{ m}$
4. $73.5 \text{ m}$

Solution:

$\text{The ball falls freely for } 4.9 \text{ m, so the time taken to reach the water is } t_1 = \sqrt{\frac{2 \times 4.9}{9.8}} = 1 \text{ s.}$ $\text{The remaining time to reach the bottom is } t_2 = 4.0 - 1 = 3.0 \text{ s.}$ $\text{The velocity } v \text{ when hitting the water is } v = 9.8 \times 1 = 9.8 \text{ m/s.}$ $\text{The depth of the lake is } d = v \times t_2 = 9.8 \times 3.0 = 29.4 \text{ m.}$

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
}