Import Question JSON

Current Question (ID: 20017)

Question:

$\text{In the sonometer experiment, a string of mass } 18 \text{ g having linear}$ $\text{mass density } 20 \text{ g/m oscillates in the fundamental mode (of}$ $\text{frequency } 50 \text{ Hz). The velocity of transverse waves in the string is:}$ $1.\ 70 \text{ m/s}$ $2.\ 60 \text{ m/s}$ $3.\ 90 \text{ m/s}$ $4.\ 110 \text{ m/s}$

Options:

1. $70 \text{ m/s}$
2. $60 \text{ m/s}$
3. $90 \text{ m/s}$
4. $110 \text{ m/s}$

Solution:

$\text{Hint: } f = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$ $\text{Step: Find the velocity of the transverse wave in the string.}$ $\text{The fundamental mode of frequency of the string is given by;}$ $f = \frac{1}{2l} \sqrt{\frac{T}{\mu}} = \frac{v}{2l} \ldots (1)$ $\text{The length of the string is given by; } \frac{m}{m/l} = \frac{18}{20} = 0.9 \text{ m}$ $\text{The velocity of the transverse wave in the string from the (1) equation is given by;}$ $v = 2lf = 2 \times 0.9 \times 50 = 90 \text{ m/s}$ $\text{Therefore, the velocity of the transverse wave in the string is } 90 \text{ m/s.}$ $\text{Hence, option (3) is the correct answer.}$

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
}