Import Question JSON

Current Question (ID: 19160)

Question:

$\text{A car moving with a constant speed of } 2 \text{ m/s in a circle having a radius } R. \text{ A pendulum is suspended from the ceiling of the car. The angle made by the pendulum with vertical is:}$ $\text{(Take } R = \frac{8}{15} \text{ m and } g = 10 \text{ m/s}^2.)$

Options:

1. $30^\circ$
2. $53^\circ$
3. $37^\circ$
4. $60^\circ$

Solution:

$T \sin \theta = \frac{mv^2}{R}$ $T \cos \theta = mg$ $\tan \theta = \frac{v^2}{Rg} = \frac{4}{\frac{8}{15} \times 10} = \frac{3}{4}$ $\theta = 37^\circ$

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
}