Import Question JSON

Current Question (ID: 10153)

Question:

$\text{To maintain a rotor at a uniform angular speed of 200 rad s}^{-1}, \text{ an engine needs to transmit a torque of 180 N-m. What is the power required by the engine?}$

Options:

1. $33 \text{ kW}$
2. $36 \text{ kW}$
3. $28 \text{ kW}$
4. $76 \text{ kW}$

Solution:

$\text{Hint: The power is the work done per unit time by the torque.}$ $\text{The angular speed of the rotor is 200 rad/s.}$ $\text{The torque needed to be transmitted by the engine is 180 N-m.}$ $\text{Step 1: Find the power required.}$ $\text{The power of the rotor required to transmit energy by applying torque } \tau \text{ to the rotating motor with a given angular speed } \omega,$ $P = \tau\omega$ $= 180 \times 200 \text{ W}$ $= 36 \text{ kW}$

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
}