Import Question JSON

Current Question (ID: 19162)

Question:

$\text{A block is sliding down an inclined plane of inclination } 30^\circ, \text{ with an acceleration of } \frac{g}{4}. \text{ The coefficient of friction between the block and incline is:}$

Options:

1. $\frac{1}{\sqrt{3}}$
2. $\frac{1}{2\sqrt{3}}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Solution:

$\text{Hint: } f = \mu N$ $\text{Step 1: Draw the FBD for the given situation.}$ $a = \frac{g}{4}$ $\mu mg \cos \theta$ $mg \sin \theta$ $\text{Step 2: Find the coefficient of friction between the block and incline.}$ $\text{Balancing force gives:}$ $mg \sin \theta - \mu mg \cos \theta = ma$ $\frac{g}{4} = g \sin \theta - \mu g \cos \theta$ $\mu = \frac{1}{2\sqrt{3}}$

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
}