Import Question JSON

Current Question (ID: 10399)

Question:

$\text{A metallic rope of diameter 1 mm breaks at 10 N force. If the wire of the same material has a diameter of 2 mm, then the breaking force is:}$

Options:

1. $2.5 \text{ N}$
2. $5 \text{ N}$
3. $20 \text{ N}$
4. $40 \text{ N}$

Solution:

\text{Young's modulus of the rope: } Y = \frac{\text{stress}}{\text{strain}} = \frac{T/A}{\Delta l/l} \text{Rearranging: } T = Y \times \frac{\Delta l}{l} \times \frac{\pi d^2}{4} \text{Therefore: } T \propto d^2 \text{This gives us: } \frac{T_1}{T_2} = \left(\frac{d_1}{d_2}\right)^2 \text{Substituting values: } T_2 = \frac{T_1 \times (d_2)^2}{(d_1)^2} = \frac{10 \times (2 \times 10^{-3})^2}{(1 \times 10^{-3})^2} \text{Calculating: } T_2 = \frac{10 \times 4 \times 10^{-6}}{1 \times 10^{-6}} = 40 \text{ N}

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
}