Import Question JSON

Current Question (ID: 9766)

Question:

$\text{A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is } \mu = 0.5\text{. The distance that the box will move relative to the belt before coming to rest on it, taking } g = 10 \text{ ms}^{-2} \text{ is:}$

Options:

1. $0.4 \text{ m}$
2. $1.2 \text{ m}$
3. $0.6 \text{ m}$
4. $\text{zero}$

Solution:

$F = \mu mg$ $\text{retardation of the block on the belt}$ $a = \frac{F}{m} = \mu g$ $\text{From } v^2 = u^2 + 2as$ $0 = 2^2 - 2(\mu g)s$ $s = \frac{4}{2 \times 0.5 \times 10} = 0.4 \text{ m}$

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
}