Import Question JSON

Current Question (ID: 19997)

Question:

$\text{The percentage increase in the speed of transverse waves produced in a stretched string when the tension is increased by } 4\% \text{ is:}$ $1. \ 4\%$ $2. \ 3\%$ $3. \ 2\%$ $4. \ 1\%$

Options:

1. $4\%$
2. $3\%$
3. $2\%$
4. $1\%$

Solution:

$\text{Hint: } v = \sqrt{\frac{T}{\mu}}$ $\text{Step: Find the percentage increase in the speed of the given wave.}$ $\text{The speed of the wave is given by:}$ $v = \sqrt{\frac{T}{\mu}}$ $\Rightarrow \frac{\Delta v}{v} \times 100 = \frac{1}{2} \left( \frac{\Delta T}{T} \times 100 \right)$ $\Rightarrow \frac{\Delta v}{v} \times 100 = \frac{1}{2} \times 4\% = 2\%$ $\text{Hence, option (3) is the correct answer.}$

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
}