Import Question JSON

Current Question (ID: 10462)

Question:

$\text{A large open tank with a square hole of side } 0.1 \text{ cm in the wall at a depth of } 0.2 \text{ m from the top is completely filled with a liquid. The rate of flow of liquid (in cm}^3\text{/s) through the hole will be:}$

Options:

1. $1$
2. $2$
3. $3$
4. $4$

Solution:

$\text{Hint: Velocity of the flow through hole at depth h from the open end is } v = \sqrt{2gh}$ $\text{Step 1: Calculate the velocity of flow through the hole.}$ $\text{Given: depth } h = 0.2 \text{ m, acceleration due to gravity } g = 10 \text{ m/s}^2$ $\text{The velocity of efflux is:}$ $v = \sqrt{2 \times 10 \times 0.2} = \sqrt{4} = 2 \text{ m/s} = 200 \text{ cm/s}$ $\text{Step 2: Calculate the volume rate of flow of liquid (in cm}^3\text{/s) through the hole.}$ $\text{Volume rate} = A \times v$ $\text{where } A = \text{area of square hole} = (0.1)^2 = 0.01 \text{ cm}^2$ $\text{Volume rate} = 0.01 \times 200 = 2 \text{ cm}^3\text{/s}$

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
}