Import Question JSON

Current Question (ID: 9891)

Question:

$\text{The principle of conservation of energy implies that:}$

Options:

1. $\text{the total mechanical energy is conserved.}$
2. $\text{the total kinetic energy is conserved.}$
3. $\text{the total potential energy is conserved.}$
4. $\text{the sum of all types of energies is conserved.}$

Solution:

$\text{The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total energy of an isolated system remains constant over time.}$ $\text{While mechanical energy (kinetic + potential) is conserved only in the absence of non-conservative forces like friction, and individual kinetic or potential energies can change during processes, the fundamental principle applies to ALL forms of energy.}$ $\text{Therefore, the correct answer is that the sum of all types of energies (kinetic, potential, thermal, chemical, nuclear, etc.) is conserved in any isolated system.}$ $\text{The final answer is } \boxed{4}$

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
}