Import Question JSON

Current Question (ID: 16019)

Question:

$\text{A cylindrical tube } (L = 125 \text{ cm}) \text{ is resonant with a tuning fork at a frequency of } 330 \text{ Hz.}$ $\text{If it is filled with water, then to get the resonance again, the minimum length of the water column will be: } (v_{\text{air}} = 330 \text{ m/s})$

Options:

1. $50 \text{ cm}$
2. $60 \text{ cm}$
3. $25 \text{ cm}$
4. $20 \text{ cm}$

Solution:

$\text{Hint: } f = (2n - 1) \frac{v}{4l}$ $\text{Step: Find the minimum height of the water column.}$ $\text{The fundamental frequency of the closed organ pipe is given by:}$ $f = (2n - 1) \frac{v}{4l}$ $\Rightarrow l = (2n - 1) \frac{v}{4f} = (2n - 1) \times \left(\frac{330}{4 \times 330}\right) = \frac{(2n-1)}{4}$ $\Rightarrow l = \frac{1}{4} \text{ m}, \frac{3}{4} \text{ m} = 25 \text{ cm}, 75 \text{ cm}$ $\text{Therefore, the minimum height of the water column is given by:}$ $\Rightarrow 125 - 75 = 50 \text{ cm}$ $\text{Hence, option (1) is the correct answer.}$

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
}