Import Question JSON

Current Question (ID: 16955)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): The bar magnet falling vertically along the axis of the horizontal coil will be having acceleration less than } g.$ $\text{Reason (R): Clockwise current induced in the coil.}$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Hint: The falling magnet induces a current opposing its motion, reducing acceleration, but the direction of the induced current depends on the magnet's pole orientation.}$ $\text{Explanation:}$ $\text{Assertion (A): The bar magnet falling vertically along the axis of the horizontal coil will be having acceleration less than } g.$ $\text{This is true. As the bar magnet falls, it induces a current in the coil according to Faraday's law. This induced current generates a magnetic field that opposes the motion of the magnet (Lenz's Law). This opposition creates a resistive force that reduces the acceleration of the falling magnet, making it less than } g.$ $\text{Reason (R): Clockwise current induced in the coil.}$ $\text{This is false as a general statement. The direction of the induced current depends on the pole of the magnet facing the coil and its motion. According to Lenz's Law, the induced current generates a magnetic field that opposes the change in magnetic flux. Therefore:}$ $\text{If the North pole of the magnet approaches the coil, the coil will induce a current that creates a north pole facing the bar magnet (to oppose the motion). The direction of the current (clockwise or counterclockwise) depends on the perspective from which you observe the coil and the magnetic pole direction. Since the assertion is true, but the reason is not universally valid or explanatory in this context.}$ $\text{Hence, option (3) is the correct answer.}$

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
}