Import Question JSON

Current Question (ID: 19582)

Question:

$\text{The velocity of the upper layer of water in a river is } 36 \text{ kmh}^{-1}. \text{ Shearing stress between horizontal layers of water is } 10^{-3} \text{ Nm}^{-2}. \text{ The depth of the river is:}$ $\text{(coefficient of viscosity of water is } 10^{-2} \text{ Pa-s)}$

Options:

1. $100 \text{ m}$
2. $200 \text{ m}$
3. $300 \text{ m}$
4. $400 \text{ m}$

Solution:

$\text{Hint: } F = \eta A \frac{\Delta v_x}{\Delta y}$ $\text{Step: Find the depth of the river.}$ $\text{The shear force in a fluid is given by:}$ $\Rightarrow F = \eta A \frac{\Delta v_x}{\Delta y}$ $\Rightarrow \frac{F}{A} = \eta \frac{\Delta v_x}{\Delta y}$ $\text{Substituting the known values we get:}$ $\Rightarrow 10^{-3} = 10^{-2} \times \frac{36 \times 1000}{h \times 3600}$ $\Rightarrow h = \frac{10^{-2} \times 36 \times 1000}{10^{-3} \times 3600} = 100 \text{ m}$ $\text{Hence, option (1) is the correct answer.}$

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
}