Import Question JSON

Current Question (ID: 10356)

Question:

$\text{The stress versus strain graphs for wires of two materials } A \text{ and } B \text{ are as shown in the figure. If } Y_A \text{ and } Y_B \text{ are the Young's moduli of the materials, then:}$

Options:

1. $Y_B = 2Y_A$
2. $Y_A = Y_B$
3. $Y_B = 3Y_A$
4. $Y_A = 3Y_B$

Solution:

$\text{Young's modulus is defined as the ratio of stress to strain in the elastic region:}$ $Y = \frac{\sigma}{\varepsilon} = \tan\theta$ $\text{where } \theta \text{ is the angle that the stress-strain curve makes with the strain axis.}$ $\text{From the graph, material } A \text{ makes an angle of } 60° \text{ with the strain axis, while material } B \text{ makes an angle of } 30°.$ $\text{Therefore:}$ $\frac{Y_A}{Y_B} = \frac{\tan\theta_A}{\tan\theta_B} = \frac{\tan 60°}{\tan 30°} = \frac{\sqrt{3}}{1/\sqrt{3}} = 3$ $\text{Hence: } Y_A = 3Y_B$

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
}