Import Question JSON

Current Question (ID: 19999)

Question:

$\text{A tuning fork } A \text{ of unknown frequency produces } 5 \text{ beats per second}$ $\text{with a fork of known frequency of } 340 \text{ Hz. When fork } A \text{ is filed, the}$ $\text{beat frequency decreases to } 2 \text{ beats per second. What is the}$ $\text{frequency of fork } A?$

Options:

1. $342 \text{ Hz}$
2. $345 \text{ Hz}$
3. $335 \text{ Hz}$
4. $338 \text{ Hz}$

Solution:

$\text{Beat frequency} = |\nu_1 - \nu_2|$ $\text{Initially beat frequency} = 5 \text{ Hz}$ $\nu_A = 340 \pm 5 = 345 \text{ Hz or } 335 \text{ Hz}$ $\text{i.e., the original frequency of the tuning fork can be either } 345 \text{ Hz or } 335 \text{ Hz.}$ $\text{After filing, the frequency of the tuning fork increases slightly.}$ $\text{Therefore, the original frequency of } A \text{ should be } 335 \text{ Hz, since the}$ $\text{new beat frequency is } 2 \text{ Hz.}$ $\text{Hence, option (3) is the correct answer.}$

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
}