Import Question JSON

Current Question (ID: 16032)

Question:

$\text{Two tuning forks, } A \text{ and } B, \text{ vibrating simultaneously produce } 5 \text{ beats. The frequency of } B \text{ is } 512 \text{ Hz. It is seen that if one arm of } A \text{ is filed a little, then the number of beats increases. The frequency of } A \text{ in Hz will be:}$

Options:

1. $502$
2. $507$
3. $517$
4. $522$

Solution:

$\text{Hint: Beat } (x) = |f_1 - f_2|$ $\text{Step: Find the frequency of the tuning fork } A.$ $\text{After filling the arm of the tuning fork, frequency increases, so } n_A \text{ increases (} \uparrow \text{). Also, it is given that beat frequency increases (i.e., } x \uparrow \text{)}$ $\text{Hence } n_A \uparrow - n_B = x \uparrow \text{ ... (i) } \rightarrow \text{ Correct}$ $n_B - n_A \uparrow = x \uparrow \text{ ... (ii) } \rightarrow \text{ Wrong}$ $\Rightarrow n_A = n_B + x = 512 + 5 = 517 \text{ Hz}$ $\text{Therefore, the frequency of the tuning fork } A \text{ is } 517 \text{ Hz.}$ $\text{Hence, option (3) is the correct answer.}$

Import JSON File

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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
}