Import Question JSON

Current Question (ID: 19649)

Question:

$\text{A rod of length } L \text{ at room temperature and uniform area of the cross-section } A, \text{ is made of a metal having a coefficient of linear expansion } \alpha/^{\circ}\text{C.}$ $\text{It is observed that an external compressive force } F, \text{ is applied on each of its ends, preventing any change in the length of the rod, when it temperature rises by } \Delta T K.$ $\text{Young's modulus } Y, \text{ for this metal is:}$

Options:

1. $\frac{F}{A \alpha \Delta T}$
2. $\frac{F}{A \alpha (\Delta T - 273)}$
3. $\frac{F}{2A \alpha \Delta T}$
4. $\frac{2F}{A \alpha \Delta T}$

Solution:

$\text{Hint: } Y = \frac{\text{Stress}}{\text{Strain}}$

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
}