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Current Question (ID: 10724)

Question:

$\text{The coefficients of linear expansion of brass and steel rods are } \alpha_1 \text{ and } \alpha_2, \text{ lengths of brass and steel rods are } l_1 \text{ and } l_2 \text{ respectively. If } (l_2 - l_1) \text{ is maintained the same at all temperatures, Which one of the following relations holds good?}$

Options:

1. $\alpha_1 l_2^2 = \alpha_2 l_1^2$
2. $\alpha_1^2 l_2 = \alpha_2^2 l_1$
3. $\alpha_1 l_1 = \alpha_2 l_2$
4. $\alpha_1 l_2 = \alpha_2 l_1$ (Correct)

Solution:

$\text{(c) According to question,}$ $\text{Coefficient of linear expansion of brass} = \alpha_1$ $\text{Coefficient of linear expansion of steel} = \alpha_2$ $\text{Length of brass and steel rods are } l_1 \text{ and } l_2 \text{ respectively.}$ $\text{As given difference in length } (l_2 - l_1) \text{ is same for all temperature.}$ $\text{So,} \quad l_2' - l_1' = l_2 - l_1$ $\Rightarrow \quad l_2(1 + \alpha_2 \Delta t) - l_1(1 + \alpha_1 \Delta t) = l_2 - l_1$ $\Rightarrow \quad l_2 \alpha_2 = l_1 \alpha_1$

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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
}