Import Question JSON

Current Question (ID: 10349)

Question:

$\text{A 1000 kg lift is tied with metallic wires of maximum safe stress of } 1.4 \times 10^8 \text{ N m}^{-2}\text{. If the maximum acceleration of the lift is } 1.2 \text{ m s}^{-2}\text{, then the minimum diameter of the wire is:}$

Options:

1. $1 \text{ m}$
2. $0.1 \text{ m}$
3. $0.01 \text{ m}$
4. $0.001 \text{ m}$

Solution:

$\text{1. Calculate Maximum Tension (T):}$ $T = m(g + a) = 1000 \text{ kg}(9.8 \text{ m/s}^2 + 1.2 \text{ m/s}^2) = 11000 \text{ N}$ $\text{2. Calculate Minimum Area (A):}$ $A = \frac{T}{\sigma_{max}} = \frac{11000 \text{ N}}{1.4 \times 10^8 \text{ N/m}^2} = 7.857 \times 10^{-5} \text{ m}^2$ $\text{3. Calculate Minimum Diameter (d):}$ $d = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4 \times 7.857 \times 10^{-5} \text{ m}^2}{\pi}} = 0.01 \text{ m}$ $\text{Answer: The minimum diameter of the wire is 0.01 m.}$

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
}