Import Question JSON

Current Question (ID: 9806)

Question:

$\text{The angle of banking for a cyclist taking a turn at a curve is given by } \tan \theta = \frac{v^n}{rg} \text{ where symbols have their usual meaning. The value of } n \text{ is:}$

Options:

1. $1$
2. $2$
3. $3$
4. $4$

Solution:

$\text{Hint: Find the angle of banking.}$ $\text{Step 1: Draw a free body diagram.}$ $\text{Step 2: Find the angle of banking.}$ $N \sin \theta = \frac{mv^2}{r}$ $N \cos \theta = mg$ $\tan \theta = \frac{v^2}{rg}$ $\text{Step 3: Find the value of } n$ $\frac{v^n}{rg} = \frac{v^2}{rg}$ $\text{On comparing,}$ $n = 2$

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
}