Import Question JSON

Current Question (ID: 8223)

Question:

$\text{The SI unit of viscosity coefficient } (\eta) \text{ is-}$

Options:

1. $\text{Pascal}$
2. $\text{Nsm}^{-2}$
3. $\text{km}^{-2}\text{s}$
4. $\text{Nm}^{-2}$

Solution:

$\text{Hint: } f = \eta A \frac{dv}{dx}$ $\text{Step 1:}$ $\text{The SI unit of viscosity coefficient } (\eta) \text{ is } \text{Nm}^{-2} \text{ or } \text{Nsm}^{-2}.$ $\text{As we know that, } f = \eta A \frac{dv}{dx}$ $\text{Where, } f = \text{force}$ $\eta = \text{viscosity coefficient}$ $\frac{dv}{dx} = \text{velocity gradient}$ $\text{Step 2:}$ $\text{Substitute SI units of } f = \text{N}, \text{ dx} = \text{m}, \text{ A} = \text{m}^2 \text{ and v} = \text{ms}^{-1}$ $\text{in above equation, to get,}$ $\eta = \frac{\text{N} \times \text{m}}{\text{m}^2 \times \text{ms}^{-1}} = \text{Nm}^{-2}\text{s}$ $\text{Hence, the SI unit of } \eta \text{ is } \text{Nsm}^{-2}$

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
}