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Current Question (ID: 19544)

Question:

$\text{In an experiment to determine Young's modulus, steel wires of five different lengths (} 1, 2, 3, 4 \text{ and } 5 \text{ m) but of the same cross-section (} 2 \text{ mm}^2) \text{ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves was plotted with the wire length and the following graph is obtained. If Young's modulus of a given steel wire is } x \times 10^{11} \text{ N/m}^2, \text{ then the value of } x \text{ is:}$

Options:

1. $1$
2. $2$
3. $3$
4. $4$

Solution:

$\text{Hint: } Y = \frac{FL}{A \Delta l}$ $\text{Step 1: Find the young's modulus of the given steel wire.}$ $Y = \frac{FL}{A \Delta L}$ $\frac{\Delta L}{F} = \frac{1}{AY} \times L$ $\text{The slope of the given graph is } \frac{1}{AY}$ $\frac{1}{AY} = \frac{0.75 \times 10^{-5}}{3}$ $Y = \frac{1}{2 \times 10^{-6} \times 0.25 \times 10^{-5}} = 2 \times 10^{11} \text{ Nm}^{-2}$ $\text{Step 2: Find the value of } x.$ $\text{On comparing-}$ $x \times 10^{11} = 2 \times 10^{11}$ $\Rightarrow x = 2$ $\text{Hence, option (2) is the correct answer.}$

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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
}