Import Question JSON

Current Question (ID: 15951)

Question:

$\text{For the travelling harmonic wave,}$ $y(x, t) = 2.0 \cos 2\pi (10t - 0.0080x + 0.35)$ $\text{where } x \text{ and } y \text{ are in cm and } t \text{ is in seconds.}$ $\text{The phase difference between the oscillatory motion of two}$ $\text{points separated by a distance of } 4 \text{ m will be:}$

Options:

1. $0.8\pi \text{ rad}$
2. $\pi \text{ rad}$
3. $6.4\pi \text{ rad}$
4. $4\pi \text{ rad}$

Solution:

$\text{Hint: Phase difference due to path difference is } \Delta \phi = \left( \frac{2\pi}{\lambda} \right) \Delta x$ $\text{Step: Calculate the phase difference between the oscillatory motion of two points.}$ $\text{As in the given equation, the coefficient of } x \text{ is } \frac{2\pi}{\lambda} = 2\pi \times 0.008$ $\text{The phase difference of the wave is given by;} \Delta \phi = \left( \frac{2\pi}{\lambda} \right) \Delta x$ $\Delta \phi = 2\pi \times 0.008 \times 400$ $\Rightarrow \Delta \phi = 6.4\pi \text{ rad}$ $\text{Hence, option (3) is the correct answer.}$

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
}