Import Question JSON

Current Question (ID: 9917)

Question:

$\text{A position-dependent force; } F = 6 + 8x - 3x^2 \text{ N acts on a small body of mass 3 kg, displacing it from } x = 0 \text{ to } x = 2 \text{ m. The work done in joule is:}$

Options:

1. $20$
2. $40$
3. $10$
4. $12$

Solution:

$\text{To find the work done, integrate the force function } F = 6 + 8x - 3x^2 \text{ from } x = 0 \text{ to } x = 2:$ $W = \int_0^2 (6 + 8x - 3x^2)dx = [6x + 4x^2 - x^3]_0^2$ $W = (6(2) + 4(2)^2 - (2)^3) - (0) = (12 + 16 - 8) = 20 \text{ J}$ $\text{The work done is 20 J.}$

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
}