Import Question JSON

Current Question (ID: 9758)

Question:

$\text{A block } B \text{ is pushed momentarily along a horizontal surface with an initial velocity } v. \text{ If } \mu \text{ is the coefficient of sliding friction between } B \text{ and the surface, the block } B \text{ will come to rest after a time:}$

Options:

1. $\frac{v}{g\mu}$
2. $\frac{g\mu}{v}$
3. $\frac{g}{v}$
4. $\frac{v}{g}$

Solution:

$\text{Hint: } \vec{v} = \vec{u} + \vec{a}t$ $\text{Step 1: Find the retardation of the block.}$ $\text{Force applied = frictional force}$ $\Rightarrow \mu mg = ma$ $\Rightarrow a = \mu g$ $\text{Step 2: Find the time to stop.}$ $\text{By using the 1st equation of motion,}$ $\Rightarrow 0 = v - \mu gt \Rightarrow t = \frac{v}{\mu g}$ $\text{Hence, option (1) is the correct answer.}$

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
}