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Current Question (ID: 9898)

Question:

Water falls from a height of 60 m at a rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? }(g = 10 \text{ m/s}^2)

Options:

1. $8.1 \text{ kW}$
2. $10.2 \text{ kW}$
3. $12.3 \text{ kW}$
4. $7.0 \text{ kW}$

Solution:

$\text{Hint: } P = \frac{mgh}{t}$ $\text{Step: Find the power generated by the turbine.}$ $\text{It is given that the losses due to the friction is 10% of the energy, so the power generated by the turbine will be:}$ $P_g = P_{in} \times \frac{90}{100}$ $\text{Since the water falls from a height 60 m and }M/t = 15 \text{ kg/s and }g = 10 \text{ m/s}^2$ $\text{The power generated can be written as:}$ $P_g = \frac{mgh}{t} \times \frac{90}{100} = \frac{15 \times 10 \times 60 \times 90}{100}$ $= 8.1 \text{ kW}$ $\text{Hence, option (1) is the correct answer.}$

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
}