Import Question JSON

Current Question (ID: 10524)

Question:

$\text{A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?}$

Options:

1. $\text{It will remain unchanged}$
2. $\text{It will rise}$
3. $\text{It will fall}$
4. $\text{First it will first rise and then fall}$

Solution:

$\text{When the steel balls are in the boat, they displace water equal to their weight according to Archimedes' principle:}$ $\rho_{ball} \times V_{ball} \times g = \rho_{water} \times V_{displaced} \times g$ $\text{As } \rho_{ball} > \rho_{water}$ $V_{displaced} > V_{ball}$ $\text{When the balls are thrown into the tank, they sink and displace water equal to their own volume.}$ $\text{Since the volume of water displaced when the balls were in the boat is greater than the volume displaced when they sink,}$ $\text{the water level falls.}$

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
}