The power of water pump is 4 kW. If `g=10 ms^(-2),` the amount of water it can raise in 1 minute to a height of 20 m is

Options

A. 100 litre
B. 1000 litre
C. 1200 litre
D. 200 litre

Answer

To solve the problem, we need to determine the amount of water that a pump with a power of 4 kW can raise to a height of 20 meters in one minute. We will use the relationship between power, work done, and potential energy.

### Step-by-Step Solution:

1. **Understand the relationship between power, work, and time:**
\[ \text{Power} (P) = \frac{\text{Work Done} (W)}{\text{Time} (t)} \]
Here, the work done by the pump is used to lift the water, which increases its potential energy.

2. **Express the work done in terms of potential energy:**
The work done to lift the water is equal to the change in potential energy:
\[ W = mgh \]
where:
- \( m \) = mass of the water (in kg)
- \( g \) = acceleration due to gravity (10 m/s²)
- \( h \) = height (20 m)

3. **Substitute the work done into the power formula:**
\[ P = \frac{mgh}{t} \]

4. **Rearrange the formula to solve for mass (m):**
\[ m = \frac{Pt}{gh} \]

5. **Convert the time from minutes to seconds:**
Since we need to calculate the mass for 1 minute, we convert it:
\[ t = 1 \text{ minute} = 60 \text{ seconds} \]

6. **Substitute the known values into the equation:**
\[ m = \frac{(4 \times 10^3 \text{ W})(60 \text{ s})}{(10 \text{ m/s}^2)(20 \text{ m})} \]

7. **Calculate the mass (m):**
\[ m = \frac{240000 \text{ J}}{200 \text{ N}} = 1200 \text{ kg} \]

8. **Convert mass to volume:**
Since the density of water is approximately \( 1 \text{ kg/L} \):
\[ \text{Volume} = \frac{m}{\text{density}} = \frac{1200 \text{ kg}}{1 \text{ kg/L}} = 1200 \text{ L} \]

### Final Answer:
The amount of water that the pump can raise in 1 minute to a height of 20 m is **1200 liters**.

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