The power of pump, which can pump 200 kg of water to a height of 50 m in 10 sec, will be

Options

A. `4xx10^(3) W`
B. `10xx10^(3)W`
C. `20xx10^(3)W`
D. None of these

Explanation

To find the power of the pump that can pump 200 kg of water to a height of 50 m in 10 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass of water, \( m = 200 \, \text{kg} \)
- Height, \( h = 50 \, \text{m} \)
- Time, \( t = 10 \, \text{s} \)

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

3. **Calculate the work done**:
- The work done in lifting the water is equal to the gravitational potential energy gained by the water, which can be calculated using the formula:
\[ W = mgh \]
where \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)).

4. **Substitute the values into the work formula**:
- Now, substituting the values into the equation:
\[ W = 200 \, \text{kg} \times 10 \, \text{m/s}^2 \times 50 \, \text{m} \]

5. **Perform the calculations**:
- Calculate \( W \):
\[ W = 200 \times 10 \times 50 = 100000 \, \text{J} \quad (\text{Joules}) \]

6. **Calculate the power**:
- Now, substitute \( W \) back into the power formula:
\[ P = \frac{W}{t} = \frac{100000 \, \text{J}}{10 \, \text{s}} = 10000 \, \text{W} \]

7. **Express the power in kilowatts**:
- Since \( 1 \, \text{kW} = 1000 \, \text{W} \):
\[ P = 10000 \, \text{W} = 10 \, \text{kW} \]

### Final Answer:
The power of the pump is \( 10 \, \text{kW} \).

---