Import Question JSON

Current Question (ID: 17512)

Question:

$\text{A light ray from the air is incident (as shown in the figure) at one end of glass}$ $\text{fibre (refractive index } \mu = 1.5) \text{ making an incidence angle of } 60^\circ \text{ on the lateral}$ $\text{surface so that it undergoes a total internal reflection. How much time would it}$ $\text{take to traverse the straight fibre of a length of 1 km?}$

Options:

1. $3.33 \, \mu s$
2. $6.67 \, \mu s$
3. $5.77 \, \mu s$
4. $3.85 \, \mu s$

Solution:

$\text{The speed of light in the glass is given by } v = \frac{c}{\mu} = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \, \text{m/s}$ $\text{Time taken to traverse 1 km is } t = \frac{\text{distance}}{\text{speed}} = \frac{1000}{2 \times 10^8} = 5 \times 10^{-6} \, \text{s} = 5 \, \mu s$

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
}