Import Question JSON

Current Question (ID: 8764)

Question:

$\text{A wire has a mass of } (0.3 \pm 0.003) \text{ grams, a radius of } (0.5 \pm 0.005) \text{ mm, and a length of } (0.6 \pm 0.006) \text{ cm. The maximum percentage error in the measurement of its density will be:}$

Options:

1. $1$
2. $2$
3. $3$
4. $4$

Solution:

$\text{Hint: } \rho = \frac{M}{V}$ $\text{Step: Find the percentage error in density.}$ $\therefore \text{Density, } \rho = \frac{M}{V} = \frac{M}{\pi r^2 L}$ $\Rightarrow \frac{\Delta \rho}{\rho} = \frac{\Delta M}{M} + 2\frac{\Delta r}{r} + \frac{\Delta L}{L}$ $= \frac{0.003}{0.3} + 2 \times \frac{0.005}{0.5} + \frac{0.006}{6}$ $= 0.01 + 0.02 + 0.01 = 0.04$ $\therefore \text{Percentage error} = \frac{\Delta \rho}{\rho} \times 100 = 0.04 \times 100 = 4\%$ $\text{Hence, option (4) is the correct answer.}$

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
}