Import Question JSON

Current Question (ID: 9727)

Question:

$\text{A particle moves in the } XY\text{-plane under the action of a force } F \text{ such that the components of its linear momentum } p \text{ at any time } t \text{ are } p_x = 2\cos t, p_y = 2\sin t. \text{ The angle between } F \text{ and } p \text{ at time } t \text{ will be:}$

Options:

1. $90°$
2. $0°$
3. $180°$
4. $30°$

Solution:

$p = 2\cos t \mathbf{i} + 2\sin t \mathbf{j}$ $F = \frac{dp}{dt} = -2\sin t \mathbf{i} + 2\cos t \mathbf{j}$ $F \cdot p = (-2\sin t)(2\cos t) + (2\cos t)(2\sin t) = 0$ $\text{Angle} = 90 \text{ degrees}$

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
}