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Current Question (ID: 10357)

Question:

$\text{The elongation } (X) \text{ of a steel wire varies with the elongating force } (F) \text{ according to the graph: (within elastic limit)}$

Options:

1. $\text{Graph 1: Hyperbolic curve (decreasing)}$
2. $\text{Graph 2: Exponential curve (increasing)}$
3. $\text{Graph 3: Exponential curve (increasing)}$
4. $\text{Graph 4: Linear relationship}$

Solution:

$\text{Within elastic limit, Hooke's law is valid, so } F \propto X.$ $\text{According to Hooke's law, the force applied to an elastic material is directly proportional to the extension produced, provided the elastic limit is not exceeded.}$ $\text{Mathematically: } F = kX$ $\text{where } k \text{ is the spring constant or force constant.}$ $\text{This relationship shows that force } F \text{ is directly proportional to elongation } X\text{, which represents a linear relationship when plotted on a graph.}$ $\text{Among the given options, only Graph 4 shows a linear relationship between } F \text{ and } X\text{, which correctly represents Hooke's law.}$ $\text{Hence, the option (4) is correct.}$

Import JSON File

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
}