Import Question JSON

Current Question (ID: 9881)

Question:

$\text{The potential energy of a particle of mass 1 kg free to move along the X-axis is given by } U(x) = (3x^2 - 4x + 6) \text{ J. The force acting on the particle at x = 0 will be:}$

Options:

1. $2\hat{i} \text{ N}$
2. $-4\hat{i} \text{ N}$
3. $5\hat{i} \text{ N}$
4. $4\hat{i} \text{ N}$

Solution:

$\text{Hint: } F = -\frac{dU}{dx}$ $\text{Given: } U(x) = 3x^2 - 4x + 6$ $F = -\frac{dU}{dx} = -(6x - 4)$ $\text{At } x = 0:$ $F = -(6(0) - 4) = -(-4) = +4 \text{ N (positive x-direction)}$

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
}