Import Question JSON

Current Question (ID: 19569)

Question:

$\text{A submarine experiences a pressure of } 5.05 \times 10^6 \text{ Pa at a depth of } d_1 \text{ in a sea.}$ $\text{When it goes further to a depth of } d_2, \text{ it experiences a pressure of } 8.08 \times 10^6 \text{ Pa.}$ $\text{Then } d_2 - d_1 \text{ is approximately: (density of water } = 10^3 \text{ kg/m}^3 \text{ and acceleration due to gravity } = 10 \text{ m/s}^2)$

Options:

1. $600 \text{ m}$
2. $400 \text{ m}$
3. $300 \text{ m}$
4. $500 \text{ m}$

Solution:

$\text{Hint: } P = P_0 + h \rho g$ $\text{Step 1: Find the pressure at depth } d_1$ $P_1 = P_0 + \rho g d_1$ $\text{Step 2: Find the pressure at depth } d_2$ $P_2 = P_0 + \rho g d_2$ $\text{Step 3: Find the pressure difference between two depths}$ $\Delta P = 3.03 \times 10^6 = \rho g (\Delta d)$ $\Delta d = \frac{3.03 \times 10^6}{10^3 \times 10}$ $= 303 \text{ m}$

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
}