Import Question JSON

Current Question (ID: 10467)

Question:

$\text{There is an orifice at some depth in the water tank. Absolute pressure at the level of the orifice in the water tank is } 4 \text{ atmospheric pressure. The density of water is } 10^3 \text{ kg/m}^3 \text{ and } 1 \text{ atm pressure} = 10^5 \text{ N/m}^2. \text{ The speed of water coming out of the orifice is:}$

Options:

1. $10 \text{ m/s}$
2. $20 \text{ m/s}$
3. $10\sqrt{6} \text{ m/s}$
4. $10\sqrt{2} \text{ m/s}$

Solution:

$\text{Hint: } v_\omega = \sqrt{2gh}$ $\text{Step 1: Find the depth of the orifice inside the water tank.}$ $\text{Using the pressure equation: } P_d = P_0 + \rho gd$ $\text{where } P_d = 4 \text{ atm}, P_0 = 1 \text{ atm}, \rho = 10^3 \text{ kg/m}^3, g = 10 \text{ m/s}^2$ $4 = 1 + \rho gd$ $3 \times 10^5 = 10^3 \times 10 \times d$ $3 \times 10^5 = 10^4 \times d$ $d = 30 \text{ m}$ $\text{Step 2: Use Torricelli's formula.}$ $v = \sqrt{2gh}$ $= \sqrt{2 \times 10 \times 30}$ $= \sqrt{600}$ $= \sqrt{100 \times 6}$ $= 10\sqrt{6} \text{ m/s}$

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
}