Import Question JSON

Current Question (ID: 8757)

Question:

$\text{The percentage errors in the measurement of mass and speed are 2\% and 3\% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:}$

Options:

1. $11\%$
2. $8\%$
3. $5\%$
4. $1\%$

Solution:

$\text{Hint: Recall the percentage error.}$ $\text{Step: Find the maximum error in the estimation of the kinetic energy.}$ $\text{The kinetic energy of the particle is given by; } E = \frac{1}{2}mv^2$ $\left( \frac{\Delta E}{E} \times 100 \right) = \left( \frac{\Delta m}{m} \times 100 \right) + 2 \times \left( \frac{\Delta v}{v} \times 100 \right)$ $\Rightarrow \left( \frac{\Delta E}{E} \times 100 \right) = 2 + 2 \times 3 = 8\%$ $\text{Hence, option (2) is the correct answer.}$

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
}