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Current Question (ID: 10362)

Question:

$\text{The strain-stress curves of three wires of different materials are shown in the figure. } P, Q \text{ and } R \text{ are the elastic limits of the wires. The figure shows that:}$

Options:

1. $\text{Elasticity of wire } P \text{ is maximum.}$
2. $\text{Elasticity of wire } Q \text{ is maximum.}$
3. $\text{Tensile strength of } R \text{ is maximum.}$
4. $\text{None of the above is true.}$

Solution:

\text{As stress is shown on x-axis and strain on y-axis, we can say that } Y = \cot \theta = \frac{1}{\tan \theta} = \frac{1}{\text{slope}}. \text{So elasticity of wire } P \text{ is minimum and of wire } R \text{ is maximum.} \text{From the graph, wire } R \text{ has the steepest slope (smallest angle with x-axis), so it has the highest Young's modulus and maximum elasticity.} \text{Wire } P \text{ has the gentlest slope (largest angle with x-axis), so it has the lowest Young's modulus and minimum elasticity.} \text{Therefore, none of the given options correctly describes what the figure shows.}

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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
}