Import Question JSON

Current Question (ID: 10473)

Question:

$\text{An engine pumps water continuously through a hose. Water leaves the hose with a velocity } v \text{ and } m \text{ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?}$

Options:

1. $\frac{1}{2}mv^3$
2. $mv^3$
3. $\frac{1}{2}mv^2$
4. $\frac{1}{2}m^2v^2$

Solution:

$\text{Let } m \text{ is the mass per unit length then rate of mass per sec = } \frac{mx}{t} = mv$ $\text{Rate of KE = } \frac{1}{2}(mv)v^2 = \frac{1}{2}mv^3$

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
}