The power of a water pump is 2 kW. If `g = 10 m//s^2,` the amount of water it can raise in 1 min to a height of 10 m is :

Options

A. 2000 litre
B. 1000 litre
C. 100 litre
D. 1200 litre

Explanation

To solve the problem, we need to determine the amount of water that a pump with a power of 2 kW can raise to a height of 10 m in 1 minute. We will use the relationship between power, work, and time.

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power (P) is defined as the work done (W) per unit time (t). Mathematically, this is expressed as:
\[ P = \frac{W}{t} \]

2. **Work Done to Raise Water**:
The work done to raise a mass (m) of water to a height (h) against gravity (g) is given by:
\[ W = mgh \]
where:
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( h = 10 \, \text{m} \) (height).

3. **Convert Power to Watts**:
The power of the pump is given as 2 kW. We need to convert this to watts:
\[ 2 \, \text{kW} = 2 \times 10^3 \, \text{W} = 2000 \, \text{W} \]

4. **Time in Seconds**:
The time is given as 1 minute. We convert this to seconds:
\[ t = 1 \, \text{minute} = 60 \, \text{seconds} \]

5. **Rearranging the Power Formula**:
We can rearrange the power formula to solve for mass (m):
\[ P = \frac{mgh}{t} \implies m = \frac{Pt}{gh} \]

6. **Substituting Values**:
Now we substitute the known values into the equation:
\[ m = \frac{2000 \, \text{W} \times 60 \, \text{s}}{10 \, \text{m/s}^2 \times 10 \, \text{m}} \]

7. **Calculating the Mass**:
Calculate the mass:
\[ m = \frac{2000 \times 60}{10 \times 10} = \frac{120000}{100} = 1200 \, \text{kg} \]

8. **Convert Mass to Volume**:
Since the density of water is approximately \( 1000 \, \text{kg/m}^3 \), we can convert the mass of water to volume (in liters):
\[ \text{Volume} = \frac{m}{\text{Density}} = \frac{1200 \, \text{kg}}{1000 \, \text{kg/m}^3} = 1.2 \, \text{m}^3 \]
Since \( 1 \, \text{m}^3 = 1000 \, \text{liters} \):
\[ \text{Volume} = 1.2 \times 1000 = 1200 \, \text{liters} \]

### Final Answer:
The amount of water the pump can raise in 1 minute to a height of 10 m is **1200 liters**.