Import Question JSON

Current Question (ID: 19570)

Question:

$\text{A cubical block of side } 0.5 \text{ m floats on water with } 30\% \text{ of its volume under water.}$ $\text{What is the maximum weight that can be put on the block without fully submerging it underwater?}$ $\text{(take, density of water } = 10^3 \text{ kg/m}^3)$

Options:

1. $30.1 \text{ kg}$
2. $87.5 \text{ kg}$
3. $65.4 \text{ kg}$
4. $46.3 \text{ kg}$

Solution:

$\text{Hint: Density} = \frac{\text{Mass}}{\text{Volume}}$ $\text{Step 1: Find the density of the block.}$ $\rho_s (Ah) g = (0.3hA) g \rho_w$ $\Rightarrow \rho_s = 0.3 \rho_w$ $\text{Step 2: Find the maximum mass that is put on the block.}$ $mg + \rho_s Ahg = \rho_l Ahg$ $m = 0.7 \times 10^3 \times \frac{1}{4} \times \frac{1}{2} = 87.5 \text{ kg}$ $\text{Hence, option (2) is the correct answer.}$

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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
}