A pump can take out 7200 kg of water per hour from a well 100 m. deep. The power of pump, assuming its efficiency as `50%` will be

Options

A. 1 kW
B. 2 kW
C. 3 kW
D. 4 kW

Explanation

To find the power of the pump, we can follow these steps:

### Step 1: Determine the work done by the pump
The work done (W) by the pump to lift the water can be calculated using the formula for gravitational potential energy:
\[ W = mgh \]
where:
- \( m \) = mass of water (in kg)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height (in meters)

### Step 2: Convert the mass of water to a suitable unit
The problem states that the pump can take out 7200 kg of water per hour. We need to convert this to seconds since power is typically measured in watts (joules per second):
\[ \text{Mass per second} = \frac{7200 \, \text{kg}}{3600 \, \text{s}} = 2 \, \text{kg/s} \]

### Step 3: Calculate the work done per second
Now, we can calculate the work done per second (which is the power output of the pump) using the mass per second:
\[ W = mgh = (2 \, \text{kg/s}) \times (9.81 \, \text{m/s}^2) \times (100 \, \text{m}) \]
\[ W = 1962 \, \text{J/s} = 1962 \, \text{W} \]

### Step 4: Calculate the input power considering efficiency
Given that the efficiency of the pump is 50%, we can express the relationship between output power (\( P_{\text{output}} \)) and input power (\( P_{\text{input}} \)):
\[ \text{Efficiency} = \frac{P_{\text{output}}}{P_{\text{input}}} \]
Thus, we can rearrange this to find the input power:
\[ P_{\text{input}} = \frac{P_{\text{output}}}{\text{Efficiency}} \]
Substituting the values we have:
\[ P_{\text{input}} = \frac{1962 \, \text{W}}{0.5} = 3924 \, \text{W} \]

### Step 5: Convert the power to kilowatts
To express the power in kilowatts, we convert watts to kilowatts:
\[ P_{\text{input}} = \frac{3924 \, \text{W}}{1000} = 3.924 \, \text{kW} \]

### Final Answer
The power of the pump, assuming its efficiency is 50%, is approximately:
\[ \text{Power} \approx 3.92 \, \text{kW} \]

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