Import Question JSON

Current Question (ID: 19310)

Question:

$\text{A bullet of mass } 50 \text{ g is fired with a speed } 100 \text{ m/s on a plywood and emerges with } 40 \text{ m/s. The percentage loss of kinetic energy is:}$

Options:

1. $44\%$
2. $32\%$
3. $84\%$
4. $16\%$

Solution:

$\text{Initial kinetic energy, } KE_i = \frac{1}{2} m v_i^2 = \frac{1}{2} \times 0.05 \times (100)^2$ $\text{Final kinetic energy, } KE_f = \frac{1}{2} m v_f^2 = \frac{1}{2} \times 0.05 \times (40)^2$ $\text{Percentage loss of kinetic energy} = \frac{KE_i - KE_f}{KE_i} \times 100 = \frac{(0.05 \times 100^2) - (0.05 \times 40^2)}{0.05 \times 100^2} \times 100 = 84\%$

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
}