Import Question JSON

Current Question (ID: 9678)

Question:

$\text{A man standing on a road holds his umbrella at } 30° \text{ with the vertical to keep the rain away. He throws the umbrella and starts running at } 10 \text{ km/hr. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be:}$

Options:

1. $10 \text{ km/hr}$
2. $20 \text{ km/hr}$
3. $30 \text{ km/hr}$
4. $40 \text{ km/hr}$

Solution:

\text{When the man is at rest w.r.t. the ground, the rain comes to him at an angle } 30^\circ \text{ with the vertical. This is the direction of the velocity of raindrops with respect to the ground.} \text{Here } \vec{v}_{R,G} = \text{velocity of rain with respect to the ground} \vec{v}_{M,G} = \text{velocity of the man with respect to the ground} \text{and } \vec{v}_{R,M} = \text{velocity of the rain with respect to the man} \text{We have } \vec{v}_{R,G} = \vec{v}_{R,M} + \vec{v}_{M,G} \text{ ......(i)} \text{Taking horizontal components, equation (i) gives} v_{R,G} \sin 30^\circ = v_{M,G} = 10 \text{ km/hr} \text{or } v_{R,G} = \frac{10}{\sin 30^\circ} = 20 \text{ km/hr} \text{Hence, option (2) is the correct answer.}

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
}