Import Question JSON

Current Question (ID: 16839)

Question:

$\text{Two insulated rings, one of a slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially, the planes of the rings are mutually perpendicular. What happens when a steady current is set up in each of them?}$

Options:

1. $\text{the two rings rotate into a common plane.}$
2. $\text{the inner ring oscillates about its initial position.}$
3. $\text{the inner ring stays stationary while the outer one moves into the plane of the inner ring.}$
4. $\text{the outer ring stays stationary while the inner one moves into the plane of the outer ring.}$

Solution:

$\text{When there is a current in both of the coils, both the coils will have a magnetic moment and magnetic fields as well.}$ $\text{So both the coils apply torque on each other and start rotating about the same axis till their planes are common.}$ $\text{When their planes are common, there will be no torque on the coils.}$ $\text{The coils will not stop rotating about the same axis due to inertia and start oscillating about their common plane due to restoring torque.}$

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
}