Import Question JSON

Current Question (ID: 19567)

Question:

$\text{A wooden block is initially floating in a bucket of water with } \frac{4}{5} \text{ of its volume submerged.}$ $\text{When a certain amount of oil is poured into the bucket, the block is found to be just under the oil surface with half of its volume submerged in water and half in oil.}$ $\text{What is the density of the oil relative to that of water?}$

Options:

1. $0.7$
2. $0.5$
3. $0.8$
4. $0.6$

Solution:

$\text{Hint: Buoyant force } = V \rho g$ $\text{Step 1: Find the density of the block}$ $\rho_s V g = \rho_w \left( \frac{4}{5} V \right) g$ $\rho_s = \frac{4}{5} \rho_w$ $\text{Step 2: Draw the diagram when oil is poured}$ $\text{Step 3: Find the relative density of the oil.}$ $W = F_o + F_W$ $\rho_s V g = \rho_o \frac{V}{2} g + \rho_w \left( \frac{V}{2} \right) g$ $\rho_o = 0.6 \rho_w$ $\frac{\rho_o}{\rho_w} = 0.6$ $\text{Hence, option (4) is the correct answer.}$

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
}