Final answer:
Using the power of the pump and the gravitational potential energy equation, the pump can raise 12.8 L/min of water to a height of 10 m, thus option D is correct.
Step-by-step explanation:
The power of a motor pump (2 kW) can be used to determine how much water it can raise to a certain height in a given time frame. The required formula to calculate the flow rate of water takes into consideration the gravitational potential energy (GPE) given by the equation GPE = mass x gravitational acceleration (g) x height. The power is the work done per unit time, and since lifting water increases its gravitational potential energy, the power can be expressed as Power = (mass x g x height) / time. To find the mass flow rate (which can be converted to volume flow rate using the density of water), we rearrange the equation to mass / time = Power / (g x height).
In this question, we have a power (P) of 2 kW (2000 W), a gravitational acceleration (g) of 9.8 m/s2, and a lifting height (h) of 10m. Substituting these values into the formula, we find the mass flow rate and then convert this into a volume flow rate (m3/s) by dividing by the density of water (1000 kg/m3). Finally, we convert m3/s to liters per minute (L/min) since 1 m3 = 1000 L and there are 60 seconds in a minute.
Calculations show that the pump can raise 12.8 L/min of water to a height of 10 m under the given conditions, making option D correct.