Import Question JSON

Current Question (ID: 19198)

Question:

$\text{Two billiard balls of mass } 0.05 \text{ kg each moving in opposite directions with } 10 \text{ ms}^{-1} \text{ collide and rebound with same speed.}$ $\text{If the time duration of contact is } t = 0.005 \text{ s, then what is the force exerted on the ball due to each other?}$

Options:

1. $100 \text{ N}$
2. $200 \text{ N}$
3. $300 \text{ N}$
4. $400 \text{ N}$

Solution:

$\text{The change in velocity } \Delta v = 10 - (-10) = 20 \text{ ms}^{-1}.$ $\text{Impulse } = m \Delta v = 0.05 \times 20 = 1 \text{ Ns}.$ $\text{Force } F = \frac{\text{Impulse}}{t} = \frac{1}{0.005} = 200 \text{ N}.$

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
}