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Current Question (ID: 10424)

Question:

$\text{A wire of negligible mass and length 2 m is stretched by hanging a 20 kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is 50 J, then the strain produced in the wire will be:}$

Options:

1. $0.5$
2. $0.1$
3. $0.4$
4. $0.25$

Solution:

\text{Given:} \text{Original length } L = 2 \text{ m} \text{Mass } m = 20 \text{ kg} \text{Work done } W = 50 \text{ J} \text{Step 1: Calculate Force (F):} \text{Assuming } g = 10 \text{ m/s}^2\text{, } F = mg = 20 \text{ kg} \times 10 \text{ m/s}^2 = 200 \text{ N} \text{Step 2: Calculate Extension (}\Delta L\text{):} \text{Work done } W = \frac{1}{2}F\Delta L 50 = \frac{1}{2} \times 200 \times \Delta L 50 = 100 \times \Delta L \Delta L = \frac{50}{100} = 0.5 \text{ m} \text{Step 3: Calculate Strain (}\varepsilon\text{):} \text{Strain } \varepsilon = \frac{\Delta L}{L} = \frac{0.5 \text{ m}}{2 \text{ m}} = 0.25 \text{The strain produced in the wire is 0.25.}

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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
}