Import Question JSON

Current Question (ID: 19402)

Question:

$\text{A solid cylinder is placed gently over an inclined plane of inclination } 60^\circ. \text{ The acceleration of the cylinder, when it starts rolling without slipping, is } \frac{g}{\sqrt{x}}, \text{ where } \mu \text{ is coefficient of friction.}$ $\left( \text{Take } g = 10 \text{ m/s}^2 \right)$

Options:

1. 3
2. 2
3. 5
4. 7

Solution:

$\text{For accelerated pure rolling } a = \frac{g \sin \theta}{\left( 1 + \frac{I}{mR^2} \right)}$ $\text{Since } a = \frac{g \sin \theta}{1 + \frac{I}{MR^2}}$ $\Rightarrow a = \frac{g}{1 + \frac{1}{2}} \times \frac{\sqrt{3}}{2} = \frac{g \frac{\sqrt{3}}{2}}{\frac{3}{2}}$ $\Rightarrow a = \frac{g}{\sqrt{3}}$

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
}