Import Question JSON

Current Question (ID: 10433)

Question:

$\text{A U tube is partially filled with water. Oil which is immiscible in water is poured into one side until the water rises by 25 cm on the other side. If the oil level is 12.5 cm higher than the water level, then the relative density of the oil is:}$

Options:

1. $0.3$
2. $0.5$
3. $0.8$
4. $1.2$

Solution:

$\text{Hint: In a stationary fluid, pressure is same at all points on the same horizontal level.}$ $\text{Step 1: Draw the diagram.}$ $\text{The diagram shows a U-tube with oil on one side and water on the other, with dimensions: 12.5 cm difference in levels, 25 cm water column, and 25 cm total height on each side.}$ $\text{Step 2: Calculate ratio of the density}$ $P_A = P_B$ $P_0 + 62.5\rho_{oil}g = P_0 + \rho_w \times 50 \times g$ $\frac{\rho_{oil}}{\rho_w} = \frac{50}{62.5} = 0.8$

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
}