Import Question JSON

Current Question (ID: 9874)

Question:

$\text{The potential energy } U \text{ of a system is given by } U = A - Bx^2 \text{ (where } x \text{ is the position of its particle and } A, B \text{ are constants). The magnitude of the force acting on the particle is:}$

Options:

1. $\text{constant}$
2. $\text{proportional to } x$
3. $\text{proportional to } x^2$
4. $\text{proportional to } \left(\frac{1}{x}\right)$

Solution:

\text{Hint: The force is given by } F = -\frac{dU}{dx} \text{Step 1: Find the expression of force} F = -\frac{dU}{dx} = 2Bx \text{Therefore: } F \propto x

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
}