Import Question JSON

Current Question (ID: 10443)

Question:

$\text{A body of density } 0.7 \text{ g/cm}^3 \text{ floats on a lake of water. The fraction of the body that is outside water is:}$

Options:

1. $30\%$
2. $70\%$
3. $25\%$
4. $50\%$

Solution:

\text{Hint: Use the law of buoyancy} \text{Step 1: Find upthrust force and weight of the body} \text{Upthrust force on the body } = V_{\text{sub}} \rho_{\text{liq}} g \text{and weight of the body } = V_{\text{body}} \rho_{\text{body}} g \text{Step 2: Weight of the body = upthrust force on the body} \text{As } V_{\text{body}} \rho_{\text{body}} g = V_{\text{sub}} \rho_{\text{liq}} g \Rightarrow \frac{\rho_{\text{body}}}{\rho_{\text{liq}}} = \frac{V_{\text{sub}}}{V_{\text{body}}} \text{Step 3:} \text{As } \rho_{\text{body}} = 0.7 \text{ g/cm}^3 \frac{V_{\text{submerged}}}{V_{\text{body}}} = 0.7 \text{So, Fraction of body outside of water } = 1 - 0.7 = 0.3 = 30\%

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
}