Import Question JSON

Current Question (ID: 9696)

Question:

$\text{It is raining at 20 m/s in still air. Now a wind starts blowing with speed 10 m/s in the north direction. If a cyclist starts moving at 10 m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:}$

Options:

1. $20 \text{ m/s}$
2. $20\sqrt{2} \text{ m/s}$
3. $10\sqrt{5} \text{ m/s}$
4. $30 \text{ m/s}$

Solution:

$\text{Given, } \vec{v_r} = -20\hat{j} \text{ m/s}$ $\vec{v_w} = 10\hat{i} \text{ m/s}$ $\text{When the wind starts blowing -}$ $\vec{v_r} = (10\hat{i} - 20\hat{j}) \text{ m/s}$ $\vec{v_m} = -10\hat{i} \text{ m/s}$ $\vec{v_{rm}} = \vec{v_r} - \vec{v_m} = 10\hat{i} - 20\hat{j} + 10\hat{i}$ $= (20\hat{i} - 20\hat{j}) \text{ m/s}$ $|\vec{v_{rm}}| = \sqrt{(20)^2 + (20)^2} = 20\sqrt{2} \text{ m/s}$

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
}