Import Question JSON

Current Question (ID: 19295)

Question:

$\text{What percentage of the kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times of its mass?}$ $\text{(Assume the collision to be a head-on elastic collision)}$

Options:

1. $50.0\%$
2. $66.6\%$
3. $55.5\%$
4. $33.3\%$

Solution:

$\text{In a head-on elastic collision, the fraction of kinetic energy transferred is given by}$ $\frac{4mM}{(m+M)^2}$ $\text{where } m \text{ is the mass of the moving particle and } M \text{ is the mass of the stationary particle.}$ $\text{Given } M = 5m, \text{ the fraction becomes } \frac{4m(5m)}{(m+5m)^2} = \frac{20m^2}{36m^2} = \frac{5}{9}.$ $\text{Thus, the percentage of kinetic energy transferred is } \frac{5}{9} \times 100\% = 55.5\%.$

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
}