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Current Question (ID: 10735)

Question:

$\text{A brass wire 1.8 m long at 27°C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of -39°C, what is the tension created in a wire with a diameter of 2.0 mm?}$ $\text{(coefficient of linear expansion of brass = } 2.0 \times 10^{-5} \text{ K}^{-1}\text{, Young's modulus of brass = } 0.91 \times 10^{11} \text{ Pa )}$

Options:

1. $3.8 \times 10^3 \text{ N}$
2. $3.8 \times 10^2 \text{ N}$ (Correct)
3. $2.9 \times 10^{-2} \text{ N}$
4. $2.9 \times 10^2 \text{ N}$

Solution:

$\text{Hint: Apply the concept of thermal expansion.}$ $\text{Step 1: Find the change in length of the wire.}$ $\text{Relative change in the length of the wire,}$ $\frac{\Delta L}{L} = \alpha \Delta T = 2.0 \times 10^{-5} \times 66 = 1.32 \times 10^{-3}$ $\text{Step 2: Find the tension developed in the wire.}$ $Y = \frac{TL}{A\Delta l}$ $T = \frac{YA\Delta l}{L} = 0.91 \times 10^{11} \times 3.14 \times (1 \times 10^{-3})^2 \times 1.32 \times 10^{-3}$

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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
}