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Current Question (ID: 10386)

Question:

$\text{If } \rho \text{ is the density of the material of a wire and } \sigma \text{ is the breaking stress, the greatest length of the wire that can hang freely without breaking is:}$

Options:

1. $\frac{2}{\rho g}$
2. $\frac{\rho}{\sigma g}$
3. $\frac{\rho g}{2\sigma}$
4. $\frac{\sigma}{\rho g}$

Solution:

$\text{The greatest length } L \text{ of a wire that can hang freely without breaking is given by the formula:}$ $L = \frac{\sigma}{\rho g}$ $\text{where:}$ $\sigma \text{ is the breaking stress of the material.}$ $\rho \text{ is the density of the material.}$ $g \text{ is the acceleration due to gravity.}$

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
}