Import Question JSON

Current Question (ID: 15966)

Question:

$\text{The speed of sound in a medium is } v. \text{ If the density of the medium is doubled at constant pressure, what will be the new speed of sound?}$

Options:

1. $\sqrt{2}v$
2. $v$
3. $\frac{v}{\sqrt{2}}$
4. $2v$

Solution:

$\text{Hint: Recall the formula for the speed of sound.}$ $\text{Step: Find the new speed of the sound.}$ $v_s = \sqrt{\frac{\gamma P}{\rho}}$ $\Rightarrow v \propto \frac{1}{\sqrt{\rho}}$ $\Rightarrow \frac{v_2}{v_1} = \sqrt{\frac{\rho_1}{\rho_2}}$ $\Rightarrow v_2 = \frac{v}{\sqrt{2}}$ $\text{Therefore, the new speed of the sound is } \frac{v}{\sqrt{2}}$ $\text{Hence, option (3) is the correct answer.}$

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
}