Import Question JSON

Current Question (ID: 9914)

Question:

$\text{A body having an initial kinetic energy 2 J collides with an identical body at rest. The maximum loss of kinetic energy in the collision will be:}$

Options:

1. $\text{2 J}$
2. $\text{Zero}$
3. $\text{1 J}$
4. $\text{1.5 J}$

Solution:

\text{Step 1: Use perfectly inelastic condition} \text{For maximum loss of kinetic energy, the collision must be perfectly inelastic.} \text{Initial: One body with mass } m \text{ and velocity } v\text{, other body at rest} \text{Final: Both bodies stick together with velocity } v_1 \text{Using conservation of momentum: } mv = 2mv_1 v_1 = v/2 \text{Step 2: Find initial and final kinetic energy} K_i = (1/2)mv^2 K_f = (1/2)(2m)(v/2)^2 = (1/2) \times (1/2)mv^2 = (1/4)mv^2 \text{Given that initial kinetic energy is 2 J, so } (1/2)mv^2 = 2 \text{ J} \text{Therefore: } K_f = (1/4)mv^2 = (1/2) \times 2 = 1 \text{ J} \text{Maximum loss of kinetic energy } = K_i - K_f = 2 - 1 = 1 \text{ J}

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
}