Import Question JSON

Current Question (ID: 16036)

Question:

$\text{Each of the two strings of lengths } 51.6 \text{ cm and } 49.1 \text{ cm is tensioned separately by } 20 \text{ N of force.}$ $\text{The mass per unit length of both strings is the same and equals } 1 \text{ g/m.}$ $\text{When both the strings vibrate simultaneously, the number of beats is:}$

Options:

1. $5$
2. $7$
3. $8$
4. $3$

Solution:

$\text{Hint: Beat frequency per second=} |f_1 - f_2|$ $\text{Step: Find the number of beats.}$ $\text{The number of beats will be the difference between the frequencies of the two strings.}$ $\text{The frequency of the first string is,}$ $f_1 = \frac{1}{2l_1} \sqrt{\frac{T}{\mu}}$ $f_1 = \frac{1}{2 \times 51.6 \times (10)^{-2}} \sqrt{\frac{20}{(10)^{-3}}}$ $f_1 = 137 \text{ Hz}$ $\text{Similarly, the frequency of the second string is, } f_2 = \frac{1}{2l_2} \sqrt{\frac{T}{\mu}}$ $f_2 = \frac{1}{2 \times 49.1 \times (10)^{-2}} \sqrt{\frac{20}{(10)^{-3}}}$ $f_2 = 144 \text{ Hz}$ $\text{So, the number of beats per second = } |f_1 - f_2|$ $\Rightarrow |137 - 144| = 7 \text{ beats}$ $\text{Hence, option (2) is the correct answer.}$

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
}