Import Question JSON

Current Question (ID: 19535)

Question:

$\text{The elastic limit of brass is } 400 \text{ MPa. What should be the minimum diameter of a brass rod if it is to support a } 400\pi \text{ N load without exceeding its elastic limit?}$ $1. \ 1 \text{ mm}$ $2. \ 1.5 \text{ mm}$ $3. \ 2 \text{ mm}$ $4. \ 2.5 \text{ mm}$

Options:

1. $1 \text{ mm}$
2. $1.5 \text{ mm}$
3. $2 \text{ mm}$
4. $2.5 \text{ mm}$

Solution:

$\text{Hint: Limiting stress } = \frac{F}{A_{\text{min}}}$ $\text{Step 1: Find the breaking stress of brass}$ $\sigma_b = 400 \text{ MPa}$ $\text{Step 2: Find the minimum diameter such that the wire doesn't break}$ $\sigma_b = \frac{F}{\pi r_{\text{min}}^2} = 400 \text{ MPa}$ $\Rightarrow \frac{400\pi}{\pi \times 400 \times 10^6} = r_{\text{min}}^2$ $r_{\text{min}} = 1 \text{ mm}$ $d_{\text{min}} = 2 \text{ mm}$

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
}