Import Question JSON

Current Question (ID: 10444)

Question:

A block weighs $5 \text{ N}$ in the air and $4.5 \text{ N}$ in a liquid of specific gravity $0.5$. Its weight in water will be:

Options:

1. $3.5 \text{ N}$
2. $4.0 \text{ N}$
3. $2.5 \text{ N}$
4. $3.0 \text{ N}$

Solution:

F_{\text{buoyancy}} = V\rho_1g \text{Step 1: Use the buoyant force equation for liquid of specific gravity } 0.5. \text{Apparent weight = Weight in air - Buoyant force} 4.5 = 5 - \rho_1 Vg \rho_1 Vg = 0.5 \text{ N} Vg = \frac{0.5}{\rho_1} \text{Step 2: Find the apparent weight in water.} W'_{\text{water}} = W_{\text{air}} - \rho_w Vg = 5 - \frac{0.5\rho_w}{\rho_1} \text{Since the specific gravity of the liquid is } 0.5, \text{ we have } \frac{\rho_1}{\rho_w} = 0.5, \text{ which means } \frac{\rho_w}{\rho_1} = \frac{1}{0.5} = 2. \text{So, } W'_{\text{water}} = 5 - 0.5 \times \frac{\rho_w}{\rho_1} = 5 - 0.5 \times 2 = 5 - 1 = 4 \text{ N}.

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
}