Import Question JSON

Current Question (ID: 19187)

Question:

$\text{A uniform chain of } 6 \text{ m in length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The coefficient of static friction between the chain and the surface of the table is } 0.5. \text{ The maximum length of the chain hanging from the table is:}$

Options:

1. $1 \text{ m}$
2. $2 \text{ m}$
3. $3 \text{ m}$
4. $4 \text{ m}$

Solution:

$\text{Let } x \text{ be the length of the chain hanging from the table.}$ $\text{The force of static friction is } f_s = \mu_s m g = 0.5 \times \frac{x}{6} \times 6g = 0.5 x g.$ $\text{For equilibrium, } xg = 0.5 x g.$ $\text{Thus, } x = 2 \text{ m.}$

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
}