Import Question JSON

Current Question (ID: 19956)

Question:

$\text{A particle executes SHM from the mean position with amplitude 'a' and time period } T. \text{ The displacement of the particle when its speed is half of the maximum speed is } \frac{\sqrt{x}}{2} a. \text{ The value of } x \text{ is:}$

Options:

1. $4$
2. $3$
3. $2$
4. $1$

Solution:

$\text{Hint: } v = \omega \sqrt{A^2 - x^2}$ $V = \omega \sqrt{A^2 - x^2} \quad V_{\text{max}} = A\omega$ $\frac{A\omega}{2} = \omega \sqrt{A^2 - x^2}$ $\frac{A^2}{4} = A^2 - x^2$ $x^2 = \frac{3A^2}{4}$ $x = \frac{\sqrt{3}}{2} A$

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
}