To solve the given problem, we need to calculate the power of the engine. Here is the step-by-step solution:
Step 1: Calculate the work done to pump the water
The work done (\(W\)) to pump the water can be calculated using the formula for gravitational potential energy:
\[ W = m \cdot g \cdot h \]
where:
- \(m = 100 \, \text{kg}\) is the mass of the water,
- \(g = 10 \, \text{m/s}^2\) is the acceleration due to gravity,
- \(h = 10 \, \text{m}\) is the height.
Substituting the values:
\[ W = 100 \, \text{kg} \times 10 \, \text{m/s}^2 \times 10 \, \text{m} \]
\[ W = 10000 \, \text{J} \]
Step 2: Calculate the total power required
Since the efficiency of the engine is 60%, the actual work output is 60% of the total work input. Let \(P_{\text{input}}\) be the total power input and \(P_{\text{output}}\) be the power output. The relationship between power input and output is:
\[ \text{Efficiency} = \frac{P_{\text{output}}}{P_{\text{input}}} \]
\[ 0.60 = \frac{P_{\text{output}}}{P_{\text{input}}} \]
\[ P_{\text{input}} = \frac{P_{\text{output}}}{0.60} \]
We need to calculate the power output first, which is the work done divided by time:
\[ P_{\text{output}} = \frac{W}{t} \]
where:
- \(W = 10000 \, \text{J}\),
- \(t = 5 \, \text{s}\).
Substituting the values:
\[ P_{\text{output}} = \frac{10000 \, \text{J}}{5 \, \text{s}} \]
\[ P_{\text{output}} = 2000 \, \text{W} \]
Step 3: Calculate the power of the engine
Using the efficiency formula, we can find the power input:
\[ P_{\text{input}} = \frac{2000 \, \text{W}}{0.60} \]
\[ P_{\text{input}} = \frac{2000}{0.60} \]
\[ P_{\text{input}} = 3333.33 \, \text{W} \]
Conclusion
The power of the engine is \(3333.33 \, \text{W}\).i.e. 3.3Kw.
So The correct Answer is option A