Given:
Volume of water lifted = 100 liters
Height lifted = 200 meters
Time taken = 1 minute
First, let's convert the volume of water from liters to cubic meters:
1 liter = 0.001 cubic meters
100 liters = 100 * 0.001 = 0.1 cubic meters
Next, let's calculate the work done using the formula:
Work = Force × Distance
Force can be calculated as the weight of the water lifted:
Weight = Mass × Acceleration due to gravity
The mass of water can be calculated using its volume and density:
Density of water = 1000 kg/m^3 (approximately)
Mass = Volume × Density
Mass = 0.1 cubic meters × 1000 kg/m^3 = 100 kg
Weight = Mass × Acceleration due to gravity
Weight = 100 kg × 9.8 m/s^2 = 980 Newtons
Now, let's calculate the work done:
Work = Force × Distance
Work = Weight × Height
Work = 980 N × 200 m = 196,000 Joules
Therefore, the work done by the pump in lifting 100 liters of water through a height of 200 meters in 1 minute is 196,000 Joules.
To calculate the work done in an hour, we need to convert the time from minutes to hours:
1 hour = 60 minutes
Since the work done in 1 minute is 196,000 Joules, the work done in 1 hour is:
Work in 1 hour = Work in 1 minute × 60
Work in 1 hour = 196,000 Joules × 60
Work in 1 hour = 11,760,000 Joules
Therefore, the correct work done by the pump in an hour is 11,760,000 Joules.