Import Question JSON

Current Question (ID: 10123)

Question:

$\text{An electric fan rotating at 1200 rpm is switched off. If the fan stops after 10 seconds, the number of revolutions completed by the fan before it stops will be: (assume uniform retardation)}$

Options:

1. $100$
2. $50$
3. $40$
4. $20$

Solution:

\text{Step 1: Find initial angular speed in rad/sec.} \omega_0 = 1200 \times \frac{2\pi}{60} = 40\pi \text{ rad/s} \text{Step 2: Find the angular retardation} \omega = \omega_0 + \alpha t 0 = 40\pi - 10\alpha \alpha = 4\pi \text{ rad/s}^2 \text{Step 3: Find the stopping angle.} \theta_s = \frac{\omega_0^2}{2\alpha} = \frac{(40\pi)^2}{2(4\pi)} = \frac{1600\pi^2}{8\pi} = 200\pi \text{Step 4: Find the number of revolutions before stopping.} \text{No. of revolutions} = \frac{\theta}{2\pi} = \frac{200\pi}{2\pi} = 100

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
}