Import Question JSON

Current Question (ID: 19550)

Question:

$\text{A uniform wire has length } L \text{ and radius } r. \text{ It is acted on by a force } F \text{ as shown. The elongation is } \Delta L. \text{ If } F \text{ and } r \text{ are both halved, then the new elongation will be:}$

Options:

1. $\frac{\Delta L}{2}$
2. $\Delta L$
3. $4\Delta L$
4. $2\Delta L$

Solution:

$\text{Hint: } Y = \frac{F \cdot L}{A \cdot \Delta L}$ $\Delta L = \frac{FL}{AY} \propto \frac{F}{r^2}$ $\Rightarrow \Delta L' = \left(\frac{1}{2}\right) \left(\frac{1}{2}\right)^2 \Delta L = 2\Delta L$

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
}