Import Question JSON

Current Question (ID: 9901)

Question:

A quarter horse-power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be:

Options:

1. $7.46 \text{ J}$
2. $7400 \text{ J}$
3. $7.46 \text{ ergs}$
4. $74.6 \text{ J}$

Solution:

$\text{Motor makes 600 revolution per minute}$ $\therefore n = 600 \frac{\text{revolution}}{\text{minute}} = 10 \frac{\text{rev}}{\text{sec}}$ $\therefore \text{Time required for one revolution} = \frac{1}{10} \text{sec}$ $\text{Energy required for one revolution = power × time}$ $= \frac{1}{4} \times 746 \times \frac{1}{10} = \frac{746}{40} \text{ J}$ $\text{But work done = 40% of input}$ $= 40\% \times \frac{746}{40} = \frac{40}{100} \times \frac{746}{40} = 7.46 \text{ J}$

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
}