Import Question JSON

Current Question (ID: 10246)

Question:

$\text{A rigid body rotates about a fixed axis with a variable angular velocity equal to } \alpha - \beta t, \text{ at the time } t, \text{ where } \alpha, \beta \text{ are constants. The angle through which it rotates before it stops is:}$

Options:

1. $\frac{\alpha^2}{2\beta}$
2. $\frac{\alpha^2-\beta^2}{2\alpha}$
3. $\frac{\alpha^2-\beta^2}{2\beta}$
4. $\frac{(\alpha-\beta)\alpha}{2}$

Solution:

$\omega = \alpha - \beta t. \text{ Comparing with } \omega = \omega_0 - \alpha t$ $\text{initial angular velocity } = \alpha$ $\text{Angular retardation } = \beta$ $\therefore \text{ Angle rotated before it stops is } \frac{\alpha^2}{2\beta}$ $\text{From, } 0 = \alpha^2 - 2\beta\theta$

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
}