Import Question JSON

Current Question (ID: 10130)

Question:

$\text{A particle rotating on a circular path of the radius } \frac{4}{\pi} \text{ m at 300 rpm reaches 600 rpm in 6 revolutions. If the angular velocity increases at a constant rate, find the tangential acceleration of the particle:}$

Options:

1. $10 \text{ m/s}^2$
2. $12.5 \text{ m/s}^2$
3. $25 \text{ m/s}^2$
4. $50 \text{ m/s}^2$

Solution:

\text{Given:} \omega_i = 2\pi \times \frac{300}{60} = 10\pi \text{ rad/sec} \omega_f = 2\pi \times \frac{600}{60} = 20\pi \text{ rad/sec} \text{Using 3rd equation of angular motion:} \omega_f^2 = \omega_i^2 + 2\alpha\theta (20\pi)^2 = (10\pi)^2 + 2 \times \alpha \times 12\pi \alpha = \frac{300\pi^2}{24\pi} = \frac{25\pi}{2} \text{ rad/sec}^2 \text{Tangential acceleration} = R \cdot \alpha = \frac{4}{\pi} \times \frac{25\pi}{2} = 50 \text{ m/s}^2

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
}