Import Question JSON

Current Question (ID: 15965)

Question:

$\text{A transverse wave moves from a medium } A \text{ to a medium } B. \text{ In medium } A, \text{ the velocity of the transverse wave is } 500 \text{ ms}^{-1} \text{ and the wavelength is } 5 \text{ m.}$ $\text{The frequency and the wavelength of the wave in medium } B \text{ when its velocity is } 600 \text{ ms}^{-1}, \text{ respectively are:}$

Options:

1. $120 \text{ Hz and } 5 \text{ m}$
2. $100 \text{ Hz and } 5 \text{ m}$
3. $120 \text{ Hz and } 6 \text{ m}$
4. $100 \text{ Hz and } 6 \text{ m}$

Solution:

$\text{Hint: } f = \frac{v}{\lambda}$ $\text{Step 1: Find the frequency of the wave.}$ $\text{Given: } v_1 = 500 \text{ m/s}, \ \lambda_1 = 5 \text{ m}$ $f = \frac{v_1}{\lambda_1} = \frac{v_2}{\lambda_2}$ $f = \frac{500}{5} = 100 \text{ Hz}$ $\text{Step 2: Find the wavelength of the wave } B.$ $\text{As the frequency of the wave remains the same.}$ $\Rightarrow \lambda_2 = \frac{600}{100} = 6 \text{ m}$ $\text{Therefore, the wavelength of the wave } B \text{ is } 6 \text{ m.}$ $\text{Hence, option (4) is the correct answer.}$

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
}