Import Question JSON

Current Question (ID: 9879)

Question:

$\text{The potential energy of a particle of mass m varies as the magnitude of the } U = ax^2 + by. \text{ The magnitude of the acceleration of the particle at (0, 3) is: (symbols have their usual meaning)}$

Options:

1. $\sqrt{\frac{b}{m}}$
2. $\sqrt{\frac{3b}{m}}$
3. $\frac{b}{m}$
4. $\text{Zero}$

Solution:

$U = ax^2 + by$ $\vec{F} = -\frac{\partial U}{\partial x}\hat{i} - \frac{\partial U}{\partial y}\hat{j} = -2ax\hat{i} - b\hat{j}$ $\Rightarrow \vec{a} = \frac{\vec{F}}{m} = \frac{(-2ax\hat{i} - b\hat{j})}{m}$ $\text{At (0, 3): } \vec{a} = -\frac{b}{m}\hat{j}$ $\text{Magnitude of the acceleration} = \frac{b}{m}$

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
}