Import Question JSON

Current Question (ID: 9838)

Question:

$\text{A position dependent force } F = 7 - 2x + 3x^2 \text{ N acts on a small body of mass 2 kg and displaces it from } x = 0 \text{ to } x = 5 \text{ m. The work done in joule is:}$

Options:

1. $70$
2. $270$
3. $35$
4. $135$

Solution:

$\text{Given: } F = 7 - 2x + 3x^2 \text{ N}$ $\text{Mass } m = 2 \text{ kg}$ $\text{Displacement from } x = 0 \text{ to } x = 5 \text{ m}$ $\text{For work done by a variable force:}$ $W = \int dW = \int F dx = \int_0^5 (7 - 2x + 3x^2) dx$ $W = \left[7x - x^2 + x^3\right]_0^5$ $W = (7 \cdot 5 - 5^2 + 5^3) - (7 \cdot 0 - 0^2 + 0^3)$ $W = (35 - 25 + 125) - 0$ $W = 135 \text{ J}$ $\text{Therefore, option (4) is the correct answer.}$

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
}