Import Question JSON

Current Question (ID: 19606)

Question:

$\text{An ideal fluid of density } 800 \text{ kgm}^{-3}, \text{ flows smoothly through a bent pipe (as shown in the figure) that tapers in cross-sectional area from } a \text{ to } \frac{a}{2}. \text{ The pressure difference between the wide and narrow sections of the pipe is } 4100 \text{ Pa. At the wider section, the velocity of the fluid is } \frac{\sqrt{x}}{6} \text{ ms}^{-1}. \text{ The value of } x \text{ is: (Given: } g = 10 \text{ m}^{-2})$

Options:

1. $124$
2. $236$
3. $363$
4. $432$

Solution:

$\text{Using Bernoulli's equation:}$ $P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2$ $\text{Given: } P_1 - P_2 = 4100 \text{ Pa, } \rho = 800 \text{ kgm}^{-3}, h_1 - h_2 = 1 \text{ m}$ $v_1 = \frac{\sqrt{x}}{6} \text{ ms}^{-1}, v_2 = 2v_1$ $\text{Substitute and solve for } x$

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
}