Import Question JSON

Current Question (ID: 8924)

Question:

$\text{Two trains each of length 100 m are moving parallel towards each other at speeds 72 km/h and 36 km/h respectively. In how much time will they cross each other?}$

Options:

1. $4.5 \text{ s}$
2. $6.67 \text{ s}$
3. $3.5 \text{ s}$
4. $7.25 \text{ s}$

Solution:

$\text{Hint: } \vec{v}_{12} = \vec{v}_1 - \vec{v}_2$ $\text{Step 1: Draw a diagram of the velocity of the trains.}$ $\text{The trains are moving towards each other with velocities } v_1 \text{ and } v_2$ $\vec{v}_{21} = \vec{v}_2 - \vec{v}_1$ $= 108 \times \frac{5}{18}$ $= 30 \text{ m/s}$ $\text{The relative velocity magnitude is 30 m/s when trains move towards each other.}$ $\text{Step 2: Find the time of crossing.}$ $\text{Total distance to be covered = 100 + 100 = 200 m}$ $t = \frac{200}{30}$ $= 6.67 \text{ s}$ $\text{Hence, option (2) is the correct answer.}$

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
}