The power of a water pump is 2 kW. The amount of water (in litres) it can raise in one minute to a height of 10 m will be : $(g = 10 m/s^2)$

Question

Accepted Answer

To determine the amount of water a 2 kW pump can raise in one minute to a height of 10 meters, we need to use the concept of work and power in physics.

1. **Understanding Power and Work:**
   - Power is defined as the rate at which work is done. It is given by the formula:
     $$
     \text{Power} = \frac{\text{Work}}{\text{Time}}
     $$
   - Work done in lifting an object is given by:
     $$
     \text{Work} = \text{Force} \times \text{Distance}
     $$
   - The force required to lift the water is equal to the weight of the water, which is:
     $$
     \text{Force} = \text{Mass} \times g
     $$
   - Therefore, the work done in lifting the water to a height $ h $ is:
     $$
     \text{Work} = \text{Mass} \times g \times h
     $$

2. **Calculating the Mass of Water:**
   - Given that the power of the pump is 2 kW (which is 2000 watts), and the height $ h $ is 10 meters, we can rearrange the power formula to find the mass:
     $$
     \text{Power} = \frac{\text{Mass} \times g \times h}{\text{Time}}
     $$
   - Substituting the known values:
     $$
     2000 = \frac{\text{Mass} \times 10 \times 10}{60}
     $$
   - Solving for mass:
     $$
     2000 \times 60 = \text{Mass} \times 100
     $$
     $$
     \text{Mass} = \frac{2000 \times 60}{100} = 1200 \text{ kg}
     $$

3. **Converting Mass to Volume:**
   - Since the density of water is 1 kg/L, the mass of 1200 kg corresponds to 1200 liters of water.

4. **Conclusion:**
   - Therefore, the pump can raise 1200 liters of water in one minute to a height of 10 meters, which confirms that Option 3 is correct.

5. **Explanation of Incorrect Options:**
   - **Option 1 (100 liters):** This is incorrect because the calculations show that the pump can raise significantly more water than 100 liters.
   - **Option 2 (1000 liters):** This is incorrect because the calculated amount of water is 1200 liters, not 1000 liters.
   - **Option 4 (2000 liters):** This is incorrect because the pump's power is not sufficient to raise 2000 liters of water to the specified height in one minute.

By following the calculations and logical reasoning, we can confidently support Option 3 as the correct answer.