Import Question JSON

Current Question (ID: 20071)

Question:

$\text{The bob of a simple pendulum has mass } 2 \text{ g and a charge of } 5.0 \, \mu\text{C.}$ $\text{It is at rest in a uniform horizontal electric field of intensity } 2000 \, \text{V/m.}$ $\text{At equilibrium, the angle that the pendulum makes with the vertical is: (take } g = 10 \, \text{m/s}^2)$

Options:

1. $\tan^{-1}(5.0)$
2. $\tan^{-1}(0.5)$
3. $\tan^{-1}(0.2)$
4. $\tan^{-1}(2.0)$

Solution:

$\text{Hint: Balance the forces along horizontal and vertical directions.}$ $\tan \theta = \frac{qE}{Mg} = \frac{5 \times 10^{-6} \times 2 \times 10^3}{2 \times 10^{-3} \times 10} = \frac{1}{2}$ $\Rightarrow \theta = \tan^{-1}\left(\frac{1}{2}\right)$

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
}