Import Question JSON

Current Question (ID: 20635)

Question:

$50 \text{ W/m}^2$ $\text{energy density of sunlight is normally incident on the surface of a polar panel. Some part of incident energy (25\%) is reflected from the surface and the rest is absorbed. The force exerted on } 1 \text{ m}^2 \text{ surface area will be close to } (c = 3 \times 10^8 \text{ m/s}):$

Options:

1. $20 \times 10^{-8} \text{ N}$
2. $35 \times 10^{-8} \text{ N}$
3. $10 \times 10^{-8} \text{ N}$
4. $15 \times 10^{-8} \text{ N}$

Solution:

$\text{Hint: } F_{\text{reflection}} = \frac{2I}{c}$ $F = \frac{2I}{c} \ldots (\text{Reflection})$ $= \frac{I}{c} \ldots (\text{absorption})$ $F = \frac{25}{100} \left( \frac{2I}{c} \right) + \frac{75}{100} \left( \frac{I}{c} \right)$ $= \frac{125}{100} \left( \frac{I}{c} \right)$ $= \frac{125}{100} \times \frac{50}{3 \times 10^8}$ $= 20.8 \times 10^{-8} \text{ N}$

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
}