Import Question JSON

Current Question (ID: 9808)

Question:

$\text{The banking angle for a curved road of radius 490 m for a vehicle moving at 35 m/s is:}$

Options:

1. $\tan^{-1}(0.25)$
2. $\tan^{-1}(0.55)$
3. $\tan^{-1}(0.45)$
4. $\tan^{-1}(0.75)$

Solution:

$\text{Hint: Horizontal component of normal will provide the centripetal force.}$ $\text{Step 1: Break the normal reaction into two components i.e., the horizontal component and the vertical component as shown in the figure.}$ $\text{Step 2: From the diagram:}$ $N \cos \theta = Mg \quad \ldots(1)$ $N \sin \theta = \frac{Mv^2}{R} \quad \ldots(2)$ $\text{Step 3: From (1) and (2), we get:}$ $\frac{v^2}{Rg} = \tan \theta$ $\tan \theta = \frac{(35)^2}{490 \times 10}$ $\tan \theta = \frac{1225}{4900} = \frac{25}{100} = 0.25$ $\theta = \tan^{-1}(0.25)$

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
}