Import Question JSON

Current Question (ID: 10310)

Question:

$\text{A wheel is rotating about an axis through its centre at 720 rpm. It is acted upon by a constant torque opposing its motion for 8 seconds to bring it to rest finally. The value of torque in (N-m) is:}$ $\text{(given } I = \frac{24}{\pi} \text{ kg.m}^2\text{)}$

Options:

1. $48$
2. $72$
3. $96$
4. $120$

Solution:

$n = 720 \text{ rpm} = \frac{720}{60} = 12 \text{ rps}$ $\therefore \omega_0 = 2\pi \times 12 = 24\pi \text{ rad/sec}$ $\text{and } \omega = 0$ $\text{applying } \omega = \omega_0 + \alpha t$ $0 = 24\pi + \alpha \times 8$ $\alpha = -3\pi \text{ rad/sec}^2$ $\tau = I\alpha = \frac{24}{\pi} \times 3\pi = 72 \text{ Nm}$

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
}