Import Question JSON

Current Question (ID: 10476)

Question:

$\text{There is a hole in the bottom of a tank having water. If the total pressure at the bottom is 3 atm (1 atm = } 10^5 \text{ N/m}^2\text{), then the velocity of water flowing from the hole is:}$

Options:

1. $\sqrt{400} \text{ m/s}$
2. $\sqrt{600} \text{ m/s}$
3. $\sqrt{60} \text{ m/s}$
4. $\text{none of these}$

Solution:

$\text{Pressure at the bottom of tank = } 3 \times 10^5 \frac{\text{N}}{\text{m}^2} = P_{\text{atm}} + \rho gh$ $\text{Pressure due to liquid column,}$ $P_l = \rho gh = 3 \times 10^5 - 1 \times 10^5 = 2 \times 10^5 \text{ N/m}^2$ $\text{Using Torricelli's law: } P_o + 0 + \rho gh = P_o + \frac{\rho v^2}{2} + 0$ $\therefore v = \sqrt{\frac{2P_l}{\rho}} = \sqrt{\frac{2 \times 2 \times 10^5}{10^3}} = \sqrt{400} \text{ m/s}$

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
}