Import Question JSON

Current Question (ID: 10359)

Question:

$\text{Three wires } A, B, C \text{ made of the same material and radius have different lengths. The graphs in the figure show the elongation-load variation. The longest wire is:}$

Options:

1. $A$
2. $B$
3. $C$
4. $\text{All of the above}$

Solution:

\text{From the stress-strain relationship and Young's modulus formula:} Y = \frac{FL}{A\Delta L} \Rightarrow \Delta L = \frac{FL}{YA} \text{Since } \frac{\Delta L}{F} \propto L \text{From the graph, we can see that the slope of each line represents } \frac{\Delta L}{F}. \text{Since all wires are made of the same material (same Young's modulus } Y\text{) and have the same radius (same cross-sectional area } A\text{), the elongation per unit load is directly proportional to the length of the wire.} \text{Observing the slopes in the graph: Wire } C \text{ has the steepest slope, followed by wire } B\text{, then wire } A \text{ has the smallest slope.} \text{Therefore, wire } C \text{ is the longest, followed by wire } B\text{, and wire } A \text{ is the shortest.}

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
}