Import Question JSON

Current Question (ID: 16870)

Question:

$\text{A 100-turn coil of wire of size } 2 \text{ cm} \times 1.5 \text{ cm is suspended between the poles of a magnet producing a field of } 1 \text{ T, inside a galvanometer. Calculate the torque on the coil due to a current of } 0.1 \text{ A passing through the coil.}$

Options:

1. $3 \times 10^{-5} \text{ N-m}$
2. $30 \text{ N-m}$
3. $3 \times 10^{-3} \text{ N-m}$
4. $3 \times 10^{-2} \text{ N-m}$

Solution:

$\text{Hint: The torque on a loop is given by, } \vec{\tau} = \vec{m} \times \vec{B}$ $\text{Step: Find the torque on the coil.}$ $\vec{\tau} = \vec{m} \times \vec{B}$ $\Rightarrow \tau = mB \sin \theta$ $\Rightarrow \tau = NiAB \sin 90^\circ$ $\Rightarrow \tau = 100 \times 0.1 \times 2 \times 1.5 \times 10^{-4} \times 1$ $\Rightarrow \tau = 3 \times 10^{-3} \text{ N-m}$ $\text{Hence, option (3) is the correct answer.}$

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
}