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. 2000 litre

Answer

To solve the problem, we need to find out how much water a pump with a power of 4 kW can raise to a height of 20 m in 1 minute.

### Step-by-Step Solution:

1. **Understand Power and Work Done**:
Power (P) is defined as the work done (W) per unit time (t). The formula is:
\[ P = \frac{W}{t} \]

2. **Relate Work Done to Potential Energy**:
When the pump raises water, it does work against gravity, which is equal to the change in potential energy (PE). The potential energy gained by raising a mass (m) to a height (h) is given by:
\[ PE = mgh \]
where \( g \) is the acceleration due to gravity.

3. **Rearranging the Power Formula**:
We can express the work done in terms of potential energy:
\[ P = \frac{mgh}{t} \]

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

5. **Substituting Values**:
- Power \( P = 4 \text{ kW} = 4000 \text{ W} \)
- Time \( t = 1 \text{ minute} = 60 \text{ seconds} \)
- Acceleration due to gravity \( g = 10 \text{ m/s}^2 \)
- Height \( h = 20 \text{ m} \)

Now substitute these values into the equation:
\[ m = \frac{4000 \times 60}{10 \times 20} \]

6. **Calculating the Mass**:
\[ m = \frac{240000}{200} = 1200 \text{ kg} \]

7. **Finding Volume of Water**:
To find the volume (V) of water, we use the density of water:
\[ V = \frac{m}{\text{density}} = \frac{1200 \text{ kg}}{1000 \text{ kg/m}^3} = 1.2 \text{ m}^3 \]

8. **Converting Volume to Liters**:
Since \( 1 \text{ m}^3 = 1000 \text{ liters} \):
\[ V = 1.2 \text{ m}^3 = 1200 \text{ liters} \]

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

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