Import Question JSON

Current Question (ID: 19237)

Question:

$\text{A small block starts slipping down from a point } B \text{ on an inclined plane } AB, \text{ which is making an angle } \theta \text{ with the horizontal. Section } BC \text{ is smooth and the remaining section } CA \text{ is rough with a coefficient of friction } \mu. \text{ It is found that the block comes to rest as it reaches the bottom (point } A) \text{ of the inclined plane. If } BC = 2AC, \text{ the coefficient of friction is given by } \mu = k \tan \theta. \text{ The value of } k \text{ is:}$

Options:

1. $4$
2. $3$
3. $2$
4. $1$

Solution:

$\text{By using the work-energy theorem;}$ $W_g + W_f = \Delta K.E$ $\Rightarrow mg \sin \theta \times 3L - f \times L = 0 \quad [\Delta K.E = 0]$ $\Rightarrow mg \sin \theta \times 3L - \mu mg \cos \theta \times L = 0 \quad [f = \mu mg \cos \theta]$ $\Rightarrow mg \sin \theta \times 3L = \mu mg \cos \theta \times L$ $\Rightarrow 3 \sin \theta = \mu \cos \theta$ $\Rightarrow \mu = 3 \tan \theta = k \tan \theta$ $\Rightarrow k = 3$ $\text{Hence, option (2) is the correct answer.}$

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
}