Import Question JSON

Current Question (ID: 19935)

Question:

$\text{A body is doing SHM with amplitude } A. \text{ When it is at } x = +\frac{A}{2}, \text{ the ratio of kinetic energy to potential energy would be:}$

Options:

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

Solution:

$\frac{K}{U} = \frac{\frac{1}{2} m \omega^2 (A^2 - x^2)}{\frac{1}{2} m \omega^2 x^2}$ $\Rightarrow \frac{K}{U} = \frac{1}{2} k^2 (A^2 - x^2) \div \frac{1}{2} k x^2$ $\Rightarrow \frac{K}{U} = \frac{A^2 - x^2}{x^2}$ $\Rightarrow \frac{K}{U} = \frac{A^2}{x^2} - 1$ $\Rightarrow \frac{K}{U} = \frac{A^2}{(A/2)^2} - 1 \quad \left[\therefore x = \frac{A}{2}\right]$ $\Rightarrow \frac{K}{U} = \frac{3}{1}$ $\text{Therefore, the ratio of kinetic energy to potential energy is } 3 : 1. \text{ Hence, option (2) is the correct answer.}$

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
}