Import Question JSON

Current Question (ID: 15977)

Question:

$\text{The speed of sound in nitrogen gas compared to that in helium gas at } 300 \text{ K is:}$

Options:

1. $\sqrt{\frac{2}{7}}$
2. $\sqrt{\frac{1}{7}}$
3. $\sqrt{\frac{3}{5}}$
4. $\sqrt{\frac{6}{5}}$

Solution:

$\text{Hint: Speed of sound in a medium } = \sqrt{\frac{\gamma RT}{M}}.$ $\text{Step 1: Find the adiabatic index for } \text{He} \text{ and } \text{N}_2.$ $\text{For } \text{N}_2 \text{ medium, } \gamma_{\text{N}_2} = \frac{7}{5}$ $\text{For } \text{He} \text{ medium, } \gamma_{\text{He}} = \frac{5}{3}$ $\text{Step 2: Find the speed of the sound in } \text{He} \text{ and } \text{N}_2 \text{ using } v = \sqrt{\frac{\gamma RT}{M}}$ $v_{\text{N}_2} = \sqrt{\frac{7RT}{5 \times 28}}$ $\text{And, } v_{\text{He}} = \sqrt{\frac{5RT}{3 \times 4}}$ $\text{Step 3: Find the required ratio.}$ $\frac{v_{\text{N}_2}}{v_{\text{He}}} = \sqrt{\frac{3}{5}}$ $\text{Hence, option (3) is the correct answer.}$

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
}