Import Question JSON

Current Question (ID: 19205)

Question:

$\text{If the momentum of a body is increased by 20\%, then its kinetic energy increases by:}$

Options:

1. $36\%$
2. $40\%$
3. $44\%$
4. $48\%$

Solution:

$\text{Let initial momentum be } p \text{ and final momentum be } p_1 = 1.2p.$ $\text{Initial kinetic energy } K = \frac{p^2}{2m}.$ $\text{Final kinetic energy } K_1 = \frac{(1.2p)^2}{2m} = \frac{1.44p^2}{2m}.$ $\text{Increase in kinetic energy } = K_1 - K = \frac{1.44p^2}{2m} - \frac{p^2}{2m} = \frac{0.44p^2}{2m}.$ $\text{Percentage increase } = \frac{0.44p^2}{2m} \times \frac{2m}{p^2} \times 100\% = 44\%.$

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
}