Import Question JSON

Current Question (ID: 10380)

Question:

$\text{If } E \text{ is the energy stored per unit volume in a wire having } Y \text{ as Young's modulus of the material, then the stress applied is:}$

Options:

1. $\sqrt{2EY}$
2. $2\sqrt{EY}$
3. $\frac{1}{2}\sqrt{EY}$
4. $\frac{1}{2}\sqrt{EY}$

Solution:

$\text{Hint: Energy stored per unit volume is given as}$ $E = \frac{1}{2} \times \text{Stress} \times \text{Strain}$ $\text{Step 1: Apply the formula}$ $E = \frac{1}{2} \times \text{Stress} \times \text{Strain}$ $\text{As } Y = \frac{\text{Stress}}{\text{Strain}}$ $\text{So,}$ $E = \frac{1}{2} \left[\text{Stress}\right] \times \frac{\text{Stress}}{Y}$ $\Rightarrow \text{Stress} = \sqrt{2EY}$

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
}