Import Question JSON

Current Question (ID: 19161)

Question:

$\text{A block is placed on a rough inclined plane with } 45^\circ \text{ inclination. If}$ $\text{minimum force required to push the block up the incline is equal to 2}$ $\text{times the minimum force required to slide the block down the}$ $\text{inclined plane, then the value of the coefficient of friction between}$ $\text{block and incline is:}$

Options:

1. 0.25
2. 1
3. 2 (Correct)
4. 3

Solution:

$F_{\text{up}} = mg \sin \theta + \mu mg \cos \theta$ $F_{\text{down}} = \mu mg \cos \theta - mg \sin \theta$ $F_{\text{up}} = 2F_{\text{down}}$ $mg \sin \theta + \mu mg \cos \theta = 2(\mu mg \cos \theta - mg \sin \theta)$ $3 \sin \theta = \mu \cos \theta$ $\mu = 3 \tan \theta$ $\mu = 3 \tan 45^\circ = 1$

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
}