Import Question JSON

Current Question (ID: 10376)

Question:

The Poisson's ratio of a material is $0.4$. If a force is applied to a wire of this material, there is a decrease in the cross-section area by $2\%$. In such a case the percentage increase in its length will be:

Options:

1. $3\%$
2. $2.5\%$
3. $1\%$
4. $0.5\%$

Solution:

$\text{Hint: Using error analysis to find maximum percentage increase in length.}$ $\text{Step 1:}$ $A = \pi r^2$ $\sigma = 0.4$ $\frac{\Delta A}{A} \times 100 = 2\left(\frac{\Delta r}{r} \times 100\right)$ $\frac{\Delta r}{r} \times 100 = -1\%$ $\text{Step 2:}$ $\text{Poison's ratio is given by :}$ $\sigma = \frac{\text{lateral strain}}{\text{longitudinal strain}}$ $\sigma = \frac{-\frac{\Delta r}{r} \times 100}{\frac{\Delta l}{l} \times 100}$ $\frac{\Delta l}{l} \times 100 = \frac{1}{0.4}$ $= 2.5\%$

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
}