Import Question JSON

Current Question (ID: 9807)

Question:

$\text{A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is of 45°, the speed of the car is:}$

Options:

1. $20 \text{ ms}^{-1}$
2. $30 \text{ ms}^{-1}$
3. $5 \text{ ms}^{-1}$
4. $10 \text{ ms}^{-1}$

Solution:

\text{Hint: A component of the normal reaction provides the centripetal force.} \text{Step 1: Find the angle of banking.} \text{The angle of banking } \tan \theta = \frac{v^2}{rg} \text{Step 2: Find the speed of the car.} \text{Given: } \theta = 45°, \, r = 90 \text{ m} \text{And } g = 10 \text{ m/s}^2 \tan 45° = \frac{v^2}{90 \times 10} v = \sqrt{90 \times 10 \times \tan 45°} \text{Speed of car, } v = 30 \text{ m/s}

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
}