Import Question JSON

Current Question (ID: 10216)

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:

$\text{The law of conservation of angular momentum states that the total angular momentum of a system remains constant when the net external torque acting on the system is zero.}$ $\text{The key condition is that the net torque must be zero, regardless of whether the net force is zero or not.}$ $\text{This is because angular momentum depends on torque, not force. A system can have forces acting on it but still conserve angular momentum if those forces produce no net torque about the axis of rotation.}$ $\text{Therefore, the correct answer is option 3: Net force may or may not be zero and net torque is zero.}$

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
}