Import Question JSON

Current Question (ID: 15959)

Question:

$\text{A steel wire has a length of } 12.0 \text{ m and a mass of } 2.10 \text{ kg. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air, at } 20^\circ\text{C (which is } 343 \text{ m/s)?}$

Options:

1. $4.3 \times 10^3 \text{ N}$
2. $3.2 \times 10^4 \text{ N}$
3. $2.06 \times 10^4 \text{ N}$
4. $1.2 \times 10^4 \text{ N}$

Solution:

$\text{Hint: The speed of the transverse wave in a string is given by } v = \sqrt{\frac{T}{\mu}}$ $\text{Step: Find the value of tension in the string.}$ $\text{The value of tension in the string is given by equating the speed of the transverse wave in the string with the speed of sound in the dry air.}$ $\Rightarrow v = \sqrt{\frac{T}{\mu}}$ $\Rightarrow T = v^2 \mu$ $\Rightarrow T = (343)^2 \times \frac{2.1}{12}$ $\Rightarrow T \approx 2.06 \times 10^4 \text{ N}$ $\text{Hence, option (3) is the correct answer.}$

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
}