Import Question JSON

Current Question (ID: 10336)

Question:

$\text{The law of conservation of angular momentum is valid when:}$

Options:

1. $\text{The net force is zero and the net torque is non-zero}$
2. $\text{The net force is non-zero and the net torque is non-zero}$
3. $\text{Net force may or may not be zero and net torque is zero}$
4. $\text{Both force and torque must be zero}$

Solution:

\text{The conservation of angular momentum is governed by the relationship between angular momentum and torque.} \text{Mathematical foundation:} \text{Angular momentum: } L = I\omega \text{Rate of change: } \frac{dL}{dt} = \tau_{net} \text{where } \tau_{net} \text{ is the net external torque.} \text{Conservation condition: For angular momentum to be conserved, } \frac{dL}{dt} = 0 \text{, which requires } \tau_{net} = 0 \text{Key insight: Torque } \tau = r \times F \text{ depends on both force and position.} \text{Examples:} \text{1. Ice skater: Non-zero friction, zero torque about vertical axis} \text{2. Satellite: Non-zero gravity, zero torque about Earth's center} \text{Conclusion: Net force can be non-zero, but net torque must be zero for conservation.}

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
}