Import Question JSON

Current Question (ID: 16008)

Question:

$\text{The number of possible natural oscillations of the air column in a pipe closed at one end of a length of } 85 \text{ cm whose frequencies lie below } 1250 \text{ Hz is:}$ $\text{(velocity of sound } 340 \text{ ms}^{-1})$

Options:

1. $4$
2. $5$
3. $7$
4. $6$

Solution:

$\text{Hint: } f_c = \frac{v}{4l}$ $\text{Step: Find the number of possible natural oscillations.}$ $f_n = \frac{nv}{4l} = \frac{n \times 340}{4 \times 85 \times 10^{-2}} = n \times 100$ $\text{Here, } n \text{ is an odd number, so for the given condition } n \text{ can go up to } n = 11 \text{ because } n = 13 \text{ condition will not be valid.}$ $n=1,3,5,7,9,11$ $\text{Therefore, the number of possible natural oscillations could be 6.}$ $\text{Hence, option (4) is the correct answer.}$

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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
}