Import Question JSON

Current Question (ID: 19268)

Question:

$\text{If a force } F \text{ applied on an object moving along the } y\text{-axis varies with the } y\text{-coordinate as } F = 3 + 2y^2. \text{ The work done in displacing the body from } y = 2 \text{ m to } y = 5 \text{ m is:}$

Options:

1. $87 \text{ J}$
2. $0$
3. $57 \text{ J}$
4. $72 \text{ J}$

Solution:

$\text{Work done} = \int_{y_1}^{y_2} F \, dy$ $= \int_{2}^{5} (3 + 2y^2) \, dy$ $= \left[ 3y + \frac{2}{3}y^3 \right]_{2}^{5}$ $= 15 + \frac{250}{3} - 6 - \frac{16}{3}$ $= 9 + \frac{234}{3}$ $= 87 \text{ J}$

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
}