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Current Question (ID: 19553)

Question:

$\text{A uniform metallic wire is elongated by } 0.04 \text{ m when subjected to a linear force } F. \text{ The elongation, if its length and diameter are doubled and subjected to the same force will be:}$

Options:

1. $1 \text{ cm}$
2. $2 \text{ cm}$
3. $3 \text{ cm}$
4. $6 \text{ cm}$

Solution:

$\text{Hint: } \Delta \ell = \frac{F \cdot \ell}{Y \cdot \pi r^2}$ $\text{Step: Find the elongation in the wire}$ $\Delta l = \frac{F \cdot l}{Y \cdot \pi r^2} \propto \frac{l}{r^2} \cdot \frac{\Delta l_2}{\Delta l_1} = \frac{l_2 r_1^2}{l_1 r_2^2} = 2 \left(\frac{1}{2}\right)^2 = \frac{1}{2} \Delta l_2 = \frac{\Delta l_1}{2} = \frac{0.04}{2} = 0.02 \text{ m}$ $\text{Hence, option (2) is the correct answer.}$

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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
}