Import Question JSON

Current Question (ID: 9825)

Question:

$\text{The kinetic energy of a body is increased by 21\%. The percentage increase in the magnitude of linear momentum of the body will be:}$

Options:

1. $10\%$
2. $20\%$
3. $\text{Zero}$
4. $11.5\%$

Solution:

\text{Hint: Kinetic energy of a body is given by } K = \frac{p^2}{2m} \text{Step: Find the initial kinetic energy, } K_i = \frac{p_i^2}{2m} \text{Final kinetic energy } K_f = 21\% \text{ of } K_i K_f = 0.21 \times K_i = 0.21 \times \frac{p_i^2}{2m} = \frac{0.21 p_i^2}{2m} \text{Also, } K_f = \frac{p_f^2}{2m} \text{Therefore: } \frac{p_f^2}{2m} = \frac{0.21 p_i^2}{2m} \Rightarrow p_f^2 = 0.21 p_i^2 \Rightarrow p_f = \sqrt{0.21} \times p_i = 1.1 p_i \text{Percentage increase in momentum} = \frac{p_f - p_i}{p_i} \times 100 = \frac{1.1 p_i - p_i}{p_i} \times 100 = \frac{0.1 p_i}{p_i} \times 100 = 10\% \text{Hence, option (1) is the correct answer.}

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
}