Import Question JSON

Current Question (ID: 16031)

Question:

$\text{Tuning fork } F_1 \text{ has a frequency of } 256 \text{ Hz and it is observed to produce } 6 \text{ beats/second with another tuning fork } F_2. \text{ When } F_2 \text{ is loaded with wax, it still produces } 6 \text{ beats/second with } F_1. \text{ The frequency of } F_2 \text{ before loading was:}$

Options:

1. $253 \text{ Hz}$
2. $262 \text{ Hz}$
3. $250 \text{ Hz}$
4. $259 \text{ Hz}$

Solution:

$\text{Hint: Beat frequency per second } = |f_1 - f_2|$ $\text{Step: Find the frequency of } F_2 \text{ before loading.}$ $\text{Given: } n_A = \text{Known frequency } = 256 \text{ Hz, } n_B = ?$ $\text{Beats } = 6 \text{ bps, which remains the same after loading.}$ $\text{Let unknown tuning fork } F_2 \text{ is loaded so } n_B \downarrow$ $\text{Hence } n_A - n_B \downarrow = x \ldots (i) \text{ Wrong}$ $n_B \downarrow - n_A = x \ldots (ii) \text{ Correct}$ $\Rightarrow n_B = n_A + x = 256 + 6 = 262 \text{ Hz.}$ $\text{Hence, option (2) is the correct answer.}$

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
}