Question

How much water a pump of 2 kW can raise in one minute to a height of 10 m? (take g = 10 m/s$^2$)

• A. 1000 litres
• B. 1200 litres
• C. 100 litres
• D. 2000 litres

Answer 1

The Correct Option is B

To determine how much water a 2 kW pump can raise in one minute to a height of 10 meters, we need to use the concept of work done in lifting an object and the relationship between power, work, and time.

1. First, let's recall the formula for work done (W) in lifting an object to a certain height: W = m \cdot g \cdot h Where:
   • m is the mass of the water (in kg),
   • g is the acceleration due to gravity (10 m/s²),
   • h is the height (in meters).
2. The power (P) of the pump is given as 2 kW. We need to convert this to watts because the SI unit of power is the watt: 2 \; \text{kW} = 2 \times 1000 = 2000 \; \text{W}
3. The relationship between power, work, and time is given by: P = \frac{W}{t} Where:
   • P is the power in watts,
   • W is the work done in joules,
   • t is the time in seconds.
   From this formula, we can express work done as: W = P \cdot t
4. We know the time is one minute, which is equal to 60 seconds. Therefore, the work done by the pump in one minute is: W = 2000 \cdot 60 = 120000 \; \text{Joules}
5. We equate the work done by the pump to the work done in raising the water: 120000 = m \cdot 10 \cdot 10
6. Solving for m, we get: m = \frac{120000}{100} = 1200 \; \text{kg}
7. The mass of water in kilograms is equivalent to its volume in liters (since 1 liter of water has a mass of approximately 1 kg under standard conditions). Therefore, the pump can raise 1200 liters of water.

Thus, the correct answer is 1200 liters.