Import Question JSON

Current Question (ID: 9864)

Question:

$\text{Select the incorrect statement about potential energy:}$

Options:

1. $\text{A change in potential energy is equal to work done against the internal conservative force.}$
2. $\text{A change in potential energy is independent of the reference point.}$
3. $\text{A change in potential energy depends on the reference frame.}$
4. $\text{The potential energy at a point is not unique.}$

Solution:

$\text{Analyzing each statement:}$ $\text{Statement 1: Correct - Change in potential energy equals work done against conservative forces.}$ $\text{Statement 2: Correct - Change in potential energy is independent of reference point since it depends only on the difference in positions.}$ $\text{Statement 3: Incorrect - Change in potential energy is independent of reference frame for conservative forces.}$ $\text{Statement 4: Correct - Potential energy depends on the choice of reference point, so absolute value is not unique.}$ $\text{Hence, option (3) is the incorrect statement.}$

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
}