Import Question JSON

Current Question (ID: 10128)

Question:

$\text{Two gear wheels that are meshed together have radii of 0.50 cm and 0.15 cm. The number of revolutions made by the smaller one when the larger one goes through 3 revolutions is:}$

Options:

1. $\text{5 revolutions}$
2. $\text{20 revolutions}$
3. $\text{1 revolution}$
4. $\text{10 revolutions}$

Solution:

$\text{Given:}$ $r_A = 0.5 \text{ cm}$ $r_B = 0.15 \text{ cm}$ $N_A = 3$ $\text{Now,}$ $\omega_A = \frac{N_A \times 2\pi r_A}{T}$ $\omega_B = \frac{N_B \times 2\pi r_B}{T}$ $\text{As } \omega_A = \omega_B$ $\Rightarrow \frac{N_A \times 2\pi r_A}{T} = \frac{N_B \times 2\pi r_B}{T}$ $\Rightarrow N_A \times r_A = N_B \times r_B$ $\Rightarrow N_B = \frac{N_A \times r_A}{r_B}$ $= \frac{3 \times 0.5}{0.15}$ $\Rightarrow N_B = 10 \text{ rev}$

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
}