Import Question JSON

Current Question (ID: 19200)

Question:

$\text{A ball of mass } 0.15 \text{ kg hits the wall with its initial speed of } 12 \text{ ms}^{-1}$ $\text{and bounces back without changing its initial speed.}$ $\text{If the force applied by the wall on the ball during the contact is } 100 \text{ N,}$ $\text{calculate the time duration of the contact of ball with the wall.}$

Options:

1. $0.018 \text{ s}$
2. $0.036 \text{ s}$
3. $0.009 \text{ s}$
4. $0.072 \text{ s}$

Solution:

$\text{The change in momentum } = m(v - (-v)) = 0.15 \times (12 - (-12)) = 0.15 \times 24 = 3.6 \text{ kg m/s}$ $\text{Time duration } = \frac{\text{Change in momentum}}{\text{Force}} = \frac{3.6}{100} = 0.036 \text{ s}$

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
}