The power of a pump, which can pump 500 kg of water to height 100 m in 10 s is

Options

A. 75 kW
B. 25 kW
C. 50 kW
D. 500 kW

Answer

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

### Step 1: Understand the formula for power
Power is defined as the work done per unit time. Mathematically, it can be expressed as:
\[ P = \frac{W}{t} \]
where \( P \) is the power, \( W \) is the work done, and \( t \) is the time taken.

### Step 2: Calculate the work done
In this case, the work done by the pump is equal to the gravitational potential energy gained by the water when it is lifted to a height \( h \). The formula for gravitational potential energy is:
\[ W = mgh \]
where:
- \( m \) is the mass of the water (500 kg),
- \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)),
- \( h \) is the height (100 m).

### Step 3: Substitute the values into the work done formula
Now we can substitute the values into the equation:
\[ W = 500 \, \text{kg} \times 10 \, \text{m/s}^2 \times 100 \, \text{m} \]

### Step 4: Calculate the work done
Calculating this gives:
\[ W = 500 \times 10 \times 100 = 500000 \, \text{J} \]

### Step 5: Calculate the power
Now, we can substitute the work done into the power formula. The time taken is 10 seconds:
\[ P = \frac{W}{t} = \frac{500000 \, \text{J}}{10 \, \text{s}} \]

### Step 6: Perform the division
Calculating this gives:
\[ P = 50000 \, \text{W} \]

### Step 7: Convert to kilowatts
Since power is often expressed in kilowatts (kW), we convert watts to kilowatts:
\[ P = \frac{50000 \, \text{W}}{1000} = 50 \, \text{kW} \]

### Final Answer
Thus, the power of the pump is **50 kW**.

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