Import Question JSON

Current Question (ID: 9809)

Question:

$\text{A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle formed by the rod with respect to the vertical is:}$

Options:

1. $\text{zero}$
2. $30°$
3. $45°$
4. $60°$

Solution:

$\text{For a plumb bob in a car moving in circular motion, the bob deflects from vertical due to the centripetal acceleration.}$ $\text{The relationship is given by:}$ $\tan \theta = \frac{v^2/r}{g} = \frac{v^2}{rg}$ $\text{Where:}$ $\text{- } v = 10 \text{ m/s (speed of car)}$ $\text{- } r = 10 \text{ m (radius of track)}$ $\text{- } g = 10 \text{ m/s}^2 \text{ (acceleration due to gravity)}$ $\text{Substituting the values:}$ $\theta = \tan^{-1}\left(\frac{v^2}{rg}\right) = \tan^{-1}\left(\frac{10 \times 10}{10 \times 10}\right)$ $\theta = \tan^{-1}(1) = 45°$

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
}