Import Question JSON

Current Question (ID: 19545)

Question:

$\text{A metal wire of length } 0.5 \text{ m and cross-sectional area } 10^{-4} \text{ m}^2 \text{ has breaking stress } 5 \times 10^8 \text{ Nm}^{-2}. \text{ A block of } 10 \text{ kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of the block will be:}$ $1. \ 15 \ \text{m/s}$ $2. \ 50 \ \text{m/s}$ $3. \ 25 \ \text{m/s}$ $4. \ 40 \ \text{m/s}$

Options:

1. $15 \ \text{m/s}$
2. $50 \ \text{m/s}$
3. $25 \ \text{m/s}$
4. $40 \ \text{m/s}$

Solution:

$\text{Hint: } T_{\text{max}} = \text{Breaking stress} \times \text{Area}$ $\text{Step: Find the maximum linear velocity of the block.}$ $\text{Breaking stress} = \frac{F_{\text{max}}}{\text{Area}} = \frac{mv^2}{R}$ $5 \times 10^8 = \frac{mv^2}{10^{-4}}$ $v^2 = \frac{5 \times 10^8 \times 10^{-4} \times 0.5}{10}$ $v = 50 \ \text{ms}^{-1}$

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
}