How much water a pump of 2 kW can raise in one minute to a height of 10 m? (take g = 10m /s²)

To determine how much water a 2 kW pump can raise in one minute to a height of 10 m, we can use the formula for power:

P = W / t

Step 1: Calculate Work Done

The work done to raise water to a height h is given by:

W = mgh

Where:
– m is the mass of the water in kilograms (kg)
– g is the acceleration due to gravity (10 m/s²)
– h is the height in meters (10 m)

Step 2: Convert Power to Work Done in One Minute

Given:
– Power, P = 2 kW = 2000 W
– Time, t = 1 minute = 60 s

Now calculate the work done:

W = P × t
W = 2000 W × 60 s
W = 120000 J

Step 3: Calculate the Mass of Water

Now we can use the work done to calculate the mass of water:

W = mgh => m = W / (gh)

Substitute known values:

m = 120000 J / (10 m/s² × 10 m)
m = 120000 / 100
m = 1200 kg

Step 4: Convert Mass to Volume

Knowing that the density of water is around 1000 kg/m³, the volume V of water lifted will be:

V = m / density
V = 1200 kg / (1000 kg/m³)
V = 1.2 m³

Converting the above value to cubic meters into liters:
Since,
1 m³ = 1000 liters,

V = 1.2 m³ × 1000 liters/m³
V = 1200 liters

Final Answer:
In one minute, the pump is able to pump 1200 liters of water up a height of 10 m.

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