Import Question JSON

Current Question (ID: 10483)

Question:

$\text{Water flows through a horizontal tube as shown in figure. If the difference in heights of water column in vertical tubes is 80 cm and the area of cross-section at A and B are 5 cm}^2 \text{ and 3 cm}^2 \text{ respectively, then the rate of flow of water at A( in cc/sec) is:-}$ $[\text{Take } g = 10 \text{ m/s}^2]$

Options:

1. $15 \times 10^2$
2. $15 \times 10^3$
3. $150$
4. $\text{None of these}$

Solution:

$\text{Hint: Use Venturi meter}$ $\text{Step 1: Calculate pressure difference}$ $\Delta P = \rho_w gh$ $\text{Step 2: Use venturi meter formula}$ $v_A = \sqrt{\frac{2\Delta P}{\rho\left[\left(\frac{A}{a}\right)^2-1\right]}} = \sqrt{\frac{2gh}{\left(\frac{A}{a}\right)^2-1}}$ $\text{Step 3: Find the volumetric flow rate}$ $V = Av$ $= Aa\sqrt{\frac{2gh}{A^2-a^2}}$ $= 5 \times 3\sqrt{\frac{2 \times 10^4 \times 80}{5^2-3^2}}$ $= 15 \times 10^2 \text{ cm}^3/\text{s}$

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
}