Import Question JSON

Current Question (ID: 10105)

Question:

$\text{Five uniform circular plates, each of diameter } D \text{ and mass } m\text{, are laid out in a pattern shown. Using the origin shown, the } y\text{-coordinate of the centre of mass of the "five-plate" system will be:}$

Options:

1. $\frac{2D}{5}$
2. $\frac{4D}{5}$
3. $\frac{D}{3}$
4. $\frac{D}{5}$

Solution:

$Y_{\text{cm}} = \frac{\sum m_i y_i}{\sum m_i}$ $= \frac{m \times 0 + m \times D + m \times 2D + m \times D + m \times 0}{m + m + m + m + m}$ $= \frac{4D}{5}$

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
}