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Current Question (ID: 10795)

Question:

$\text{A constrained steel rod of length } l\text{, area of cross-section } A\text{, Young's modulus } Y \text{ and coefficient of linear expansion } \alpha \text{ is heated through } t°\text{C. The work that can be performed by the rod when heated is:}$

Options:

1. $(YA\alpha t)(l\alpha t)$
2. $\frac{1}{2}(YA\alpha t)(l\alpha t)$ (Correct)
3. $\frac{1}{2}(YA\alpha t)\frac{1}{2}(l\alpha t)$
4. $2(YA\alpha t)(l\alpha t)$

Solution:

\text{Given formula: } W = \frac{1}{2}F \Delta l \text{where } F = YA\alpha \Delta t \text{ and } \Delta l = \alpha L \Delta t \text{Therefore: } W = \frac{1}{2}(YA\alpha \Delta t)(\alpha L \Delta t) \text{This simplifies to: } W = \frac{1}{2}YA\alpha^2 L (\Delta t)^2 \text{The work performed by the rod when heated is given by option 2.}

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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
}