Import Question JSON

Current Question (ID: 15998)

Question:

$\text{A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of } 27^\circ \text{C, two successive resonances are produced at } 20 \text{ cm and } 73 \text{ cm column length. If the frequency of the tuning fork is } 320 \text{ Hz, the velocity of sound in air at } 27^\circ \text{C is:}$

Options:

1. $330 \text{ m/s}$
2. $339 \text{ m/s}$
3. $350 \text{ m/s}$
4. $300 \text{ m/s}$

Solution:

$\text{Hint: } f = \frac{v}{\lambda}$ $\text{Step: Find the velocity of the sound in the air.}$ $\text{Two successive resonances are produced at } 20 \text{ cm and } 73 \text{ cm of column length:}$ $\frac{\lambda}{2} = (73 - 20) \times 10^{-2} \text{ m}$ $\lambda = 2 \times (73 - 20) \times 10^{-2} \text{ m}$ $\lambda = 106 \times 10^{-2} \text{ m}$ $\text{The frequency of the tuning fork, } f = \frac{v}{\lambda}$ $320 = \frac{v}{106 \times 10^{-2}}$ $\Rightarrow v = 339 \text{ m/s}$ $\text{Therefore, the velocity of the sound in the air is } 339 \text{ m/s.}$ $\text{Hence, option (2) is the correct answer.}$

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
}