Import Question JSON

Current Question (ID: 19985)

Question:

$\text{A string of mass per unit length equal to } 7 \times 10^{-3} \text{ kg/m is subjected to a tension equal to } 70 \text{ N. The speed of the transverse wave on this string is equal to:}$

Options:

1. $10 \text{ m/s}$
2. $50 \text{ m/s}$
3. $100 \text{ m/s}$
4. $200 \text{ m/s}$

Solution:

$\text{The speed of transverse waves on the wire is given by,}$ $v = \sqrt{\frac{T}{\mu}}$ $\text{Given the tension } T = 70 \text{ N, and the mass per unit length of wire } \mu = 7 \times 10^{-3} \text{ kg/m}$ $v = \sqrt{\frac{T}{\mu}}$ $v = \sqrt{\frac{70}{7 \times 10^{-3}}} = 100 \text{ m/s}$ $\text{Hence, option (3) is the correct answer.}$

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
}