Import Question JSON

Current Question (ID: 9684)

Question:

$\text{A car with a vertical windshield moves in a rain storm at a speed of 40 km/hr. The rain drops fall vertically with a constant speed of 20 m/s. The angle at which raindrops strike the windshield is:}$

Options:

1. $\tan^{-1}\frac{5}{9}$
2. $\tan^{-1}\frac{9}{5}$
3. $\tan^{-1}\frac{3}{2}$
4. $\tan^{-1}\frac{2}{3}$

Solution:

$\text{Hint: Convert all speeds in S.I. units}$ $\text{Step 1:}$ $v_C = 40 \text{ km/h}$ $= 40 \times \frac{5}{18}$ $= \frac{100}{9} \text{ m/s}$ $\text{Step 2: Draw the velocities}$ $\vec{v}_C = \frac{100}{9}\hat{i}$ $\vec{v}_R = -20\hat{j}$ $\text{Step 3: Use relative velocity concept}$ $\vec{v}_{R,C} = \vec{v}_R - \vec{v}_C$ $= -20\hat{j} - \frac{100}{9}\hat{i}$ $\tan \theta = \frac{v_C}{v_R}$ $= \frac{5}{9}$

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
}