Import Question JSON

Current Question (ID: 19643)

Question:

$\text{A compressive force } F \text{ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by } \Delta T. \text{ The net change in its length is zero. Let } l \text{ be the length of the rod, } A \text{ its area of cross-section, } Y \text{ is Young's modulus and } \alpha \text{ is coefficient of linear expansion. Then, the force } F \text{ is equal to:}$

Options:

1. $\frac{AY}{\alpha \Delta T}$
2. $AY \alpha \Delta T$
3. $l^2 Y \alpha \Delta T$
4. $l AY \alpha \Delta T$

Solution:

$\text{Hint: } Y = \frac{F}{A} \left( \frac{l}{\Delta l} \right)$

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
}