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Current Question (ID: 19529)

Question:
$\text{A man transforms into a giant such that all his linear dimensions become 9 times their original values. Assuming his density remains unchanged, the stress on his legs changes by a factor of:}$
Options:
  • 1. $9$
  • 2. $\frac{1}{9}$
  • 3. $81$
  • 4. $\frac{1}{81}$
Solution:
$\text{Hint: Stress on his legs} = \frac{\text{weight}}{\text{area}} = \frac{V \rho g}{A}$ $\text{Step: Find the factor by which the stress changes.}$ $\text{Stress}(S) \text{ is defined by:}$ $S = \frac{\text{Force}}{\text{Area}}$ $\Rightarrow S = \frac{mg}{A} = \frac{(\text{Volume} \times \text{Density}) \times g}{\text{Area}}$ $\Rightarrow S = \frac{L^3 \times \rho \times g}{L^2} = L \rho g$ $\text{As seen in the equation above, stress depends on length, density, and acceleration due to gravity.}$ $\text{Since the density remains the same and gravity is constant, stress becomes directly proportional to the length.}$ $\Rightarrow S \propto L$ $\text{Then, we can write:}$ $\frac{S_1}{S_2} = \frac{L_1}{L_2} = \frac{9L_1}{L_1} = 9$ $\Rightarrow S_1 = 9S_2$ $\text{Therefore, the stress in the leg will change by the factor of 9.}$ $\text{Hence, option (1) is the correct answer.}$

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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
}