Import Question JSON

Current Question (ID: 10461)

Question:

The diameter of a syringe is $4\text{ mm}$ and the diameter of its nozzle (opening) is $1\text{ mm}$. The syringe is placed on the table horizontally at a height of $1.25\text{ m}$. If the piston is moved at a speed of $0.5\text{ m/s}$, then considering the liquid in the syringe to be ideal, the horizontal range of liquid is: ($g = 10\text{ m/s}^2$)

Options:

1. $4\text{ m}$
2. $8\text{ m}$
3. $0.4\text{ m}$
4. $0.2\text{ m}$

Solution:

Hint: Liquid drop coming out of nozzle performs a horizontal projectile motion. Step 1: Calculate the velocity of liquid coming out of the nozzle. $A_1v_1 = A_2v_2$ $\pi\frac{(4)^2}{4} \times 0.5 = \pi\frac{(1)^2}{4} \times v_2$ $v_2 = 8\text{ m/s}$ Step 2: Notice that the fluid coming out performs a horizontal projectile motion. $R = v_2\sqrt{\frac{2h}{g}}$ $= 8\sqrt{\frac{2 \times 1.25}{10}} = 4\text{ m}$ Hence, option (1) 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
}