Import Question JSON

Current Question (ID: 19978)

Question:

$\text{A longitudinal wave is represented by } x = 10 \sin 2\pi \left(nt - \frac{x}{\lambda}\right) \text{ cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:}$

Options:

1. $2\pi \text{ cm}$
2. $5\pi \text{ cm}$
3. $\pi \text{ cm}$
4. $\frac{5\pi}{2} \text{ cm}$

Solution:

$\text{Hint: } v_p = A\omega \text{ and } v_w = n\lambda$ $\text{Step: Find the wavelength.}$ $A\omega = 4\left(\frac{\omega}{K}\right)$ $= 4\left(\frac{\omega \lambda}{2\pi}\right)$ $\lambda = \frac{\pi A}{2}$ $= 5\pi \text{ cm}$

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
}