Import Question JSON

Current Question (ID: 11243)

Question:

$\text{The total energy of a particle, executing simple harmonic motion is:}$

Options:

1. $\propto x$
2. $\propto x^2$
3. $\text{Independent of } x$ (Correct)
4. $\propto x^{\frac{1}{2}}$

Solution:

$\text{Hint: The total energy of a particle in SHM remains constant.}$ $\text{Step: Find the total energy of a particle executing SHM.}$ $\text{The total energy of a particle, executing simple harmonic motion is given by;}$ $E = \frac{1}{2}m\omega^2a^2$ $\text{This shows that the total energy } E \text{ is independent of the displacement } x.$ $\text{The total energy remains constant and does not change with the position } x \text{ of the particle.}$ $\text{Hence, option (3) is the correct answer.}$

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
}