Import Question JSON

Current Question (ID: 16893)

Question:

$\text{A closely wound solenoid of } 2000 \text{ turns and area of cross-section } 1.5 \times 10^{-4} \text{ m}^2 \text{ carries a current of } 2.0 \text{ A.}$ $\text{It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field } 5 \times 10^{-2} \text{ tesla making an angle of } 30^\circ \text{ with the axis of the solenoid.}$ $\text{The torque on the solenoid will be:}$

Options:

1. $3 \times 10^{-3} \text{ Nm}$
2. $1.5 \times 10^{-3} \text{ Nm}$
3. $1.5 \times 10^{-2} \text{ Nm}$
4. $3 \times 10^{-2} \text{ Nm}$

Solution:

$\text{Hint: } \tau = MB \sin \theta$ $\text{Step 1: Find the magnetic moment.}$ $M = niA = 2000 \times 2 \times 1.5 \times 10^{-4}$ $= 0.6 \text{ Am}^2$ $\text{Step 2: Find the torque.}$ $\tau = MB \sin \theta$ $= 0.6 \times 5 \times 10^{-2} \times \frac{1}{2}$ $= 1.5 \times 10^{-2} \text{ N} \cdot \text{m}$

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
}