Import Question JSON

Current Question (ID: 15995)

Question:

$\text{A string is stretched between fixed points separated by } 75.0 \text{ cm. It is observed to have resonant frequencies of } 420 \text{ Hz and } 315 \text{ Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for these strings is:}$

Options:

1. $155 \text{ Hz}$
2. $205 \text{ Hz}$
3. $10.5 \text{ Hz}$
4. $105 \text{ Hz}$

Solution:

$\text{Hint: } f = \frac{nv}{2L}$ $\text{Step: Find the lowest resonant frequency of the string.}$ $\text{Given: } L = 75 \text{ cm}, f_1 = 420 \text{ Hz and } f_2 = 315 \text{ Hz}$ $\text{As two consecutive resonant frequencies for a string fixed at both ends will be,}$ $f_1 = \frac{nv}{2L} \text{ and } f_2 = \frac{(n+1)v}{2L}$ $\Rightarrow f_2 - f_1 = 420 - 315$ $\Rightarrow \frac{(n+1)v}{2L} - \frac{nv}{2L} = 105 \text{ Hz}$ $\Rightarrow \frac{v}{2L} = 105 \text{ Hz}$ $\text{Therefore, the lowest resonant frequency of a string is } 105 \text{ Hz.}$ $\text{Hence, option (4) is the correct answer.}$

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
}