Import Question JSON

Current Question (ID: 15949)

Question:

$\text{The equation of a travelling wave is given as } y = A \sin(40\pi t - 0.2\pi x),$ $\text{where } t \text{ is in seconds and } x \text{ in metres.}$ $\text{The minimum distance between two particles oscillating in the same phase is:}$

Options:

1. $10 \text{ m}$
2. $5 \text{ m}$
3. $2 \text{ m}$
4. $1.5 \text{ m}$

Solution:

$\text{Hint: For the same phase } \Delta x = n \lambda.$ $\text{Step 1: Use the condition for the phase.}$ $\text{For the minimum phase, } n=1.$ $\text{i.e., } \Delta x = \lambda.$ $\text{Step 2: Write the equation of travelling wave.}$ $\text{The standard equation is } y = A \sin(\omega t - kx)$ $\text{Given equation is } y = A \sin(40\pi t - 0.2\pi x)$ $\text{Step 3: Compare the given equation with the standard equation of wave.}$ $\text{On comparing,}$ $k = 0.2\pi = \frac{2\pi}{\lambda}$ $\Rightarrow \lambda = 10 \text{ m}$ $\text{The minimum distance between two particles oscillating in the same phase is } \Delta x = \lambda = 10 \text{ m.}$ $\text{Hence, option (1) is the correct answer.}$

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
}