Import Question JSON

Current Question (ID: 19351)

Question:

$\text{The centre-of-mass of a solid hemisphere of radius } 8 \text{ cm is located at a distance of } x \text{ cm from the centre of its flat circular surface. The value of } x \text{ is:}$

Options:

1. $3$
2. $7$
3. $9$
4. $1$

Solution:

$\text{Hint: } x_{\text{com}} = \frac{\sum_{i=1}^{n} m_i x_i}{\sum_{i=1}^{n} m_i}$ $\text{Step: Find the value of } x.$ $\text{Centre of mass of a solid hemisphere of radius } R \text{ lies at a distance } \frac{3R}{8} \text{ above the centre of the flat side of hemisphere.}$ $x = \frac{3R}{8}$ $\Rightarrow x = \frac{3 \times 8}{8}$ $\Rightarrow x = 3 \text{ cm}$ $\text{Hence, Option (1) is the correct answer.}$

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
}