Import Question JSON

Current Question (ID: 9907)

Question:

$\text{A car of mass 100 kg and traveling at 20 m/s collides with a truck weighing 1 tonne traveling at 9 km/h in the same direction. The car bounces back at a speed of 5 m/s. The speed of the truck after the impact will be:}$

Options:

1. $11.5 \text{ m/s}$
2. $5 \text{ m/s}$
3. $18 \text{ m/s}$
4. $12 \text{ m/s}$

Solution:

\text{Given: } u_1 = 20 \text{ m/s}, u_2 = 9 \text{ km/h} = 9 \times \frac{5}{18} = 2.5 \text{ m/s} v_1 = -5 \text{ m/s}, v_2 = ? \text{Conserving momentum:} 100 \times 20 + 1000 \times 2.5 = 100 \times (-5) + 1000 \times v_2 2000 + 2500 = -500 + 1000 \times v_2 4500 = -500 + 1000v_2 5000 = 1000v_2 \text{Therefore: } v_2 = 5 \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
}