Import Question JSON

Current Question (ID: 9919)

Question:

$\text{A pump ejects 12,000 kg of water at a speed of 4 m/s in 40 s. The average rate at which the pump is working is:}$

Options:

1. $\text{0.24 kW}$
2. $\text{2.4 W}$
3. $\text{2.4 kW}$
4. $\text{24 W}$

Solution:

$\text{Given: mass } m = 12,000 \text{ kg, velocity } v = 4 \text{ m/s, time } t = 40 \text{ s}$ $\text{The power required to eject water is the rate of change of kinetic energy.}$ $\text{Power } P = \frac{\text{Kinetic Energy}}{\text{time}} = \frac{\frac{1}{2}mv^2}{t}$ $P = \frac{\frac{1}{2} \times 12,000 \times (4)^2}{40}$ $P = \frac{\frac{1}{2} \times 12,000 \times 16}{40}$ $P = \frac{96,000}{40} = 2,400 \text{ W} = 2.4 \text{ kW}$

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
}