Import Question JSON

Current Question (ID: 10465)

Question:

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where cross-sectional area is $10 \text{ cm}^2$, the velocity of water is $1\text{ m/s}$ and pressure is $2000\text{ Pa}$. The pressure of water at another point where cross-sectional area is $5\text{ cm}^2$, is: (Density of water=$1000\text{ kg/m}^3$)

Options:

1. $250\text{ Pa}$
2. $500\text{ Pa}$
3. $1000\text{ Pa}$
4. $2000\text{ Pa}$

Solution:

1. Use the continuity equation ($A_1v_1 = A_2v_2$) to find the new velocity ($v_2$). $(10\text{ cm}^2)(1\text{ m/s}) = (5\text{ cm}^2)v_2 \implies v_2 = 2\text{ m/s}$ 2. Use Bernoulli's equation for a horizontal pipe ($P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$) to find the new pressure ($P_2$). $2000\text{ Pa} + \frac{1}{2}(1000\text{ kg/m}^3)(1\text{ m/s})^2 = P_2 + \frac{1}{2}(1000\text{ kg/m}^3)(2\text{ m/s})^2$ $2000 + 500 = P_2 + 2000$ $2500 = P_2 + 2000$ $P_2 = 500\text{ Pa}$

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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
}