A pumping machine pumps water at a rate of 60 cc per minute at a pressure of 1.5 atm. The power delivered by the machine is

Options

A. 9 watt
B. 6 watt
C. 9 kW
D. None of these

Answer

To find the power delivered by the pumping machine, we can follow these steps:

### Step 1: Convert the given volume from cc to cubic meters
The volume of water being pumped is given as 60 cc (cubic centimeters) per minute. We need to convert this to cubic meters.

\[ 1 \text{ cc} = 1 \times 10^{-6} \text{ m}^3 \]
\[ \text{Volume} = 60 \text{ cc} = 60 \times 10^{-6} \text{ m}^3 = 60 \times 10^{-6} \text{ m}^3 \]

### Step 2: Convert the time from minutes to seconds
The time is given as 1 minute. We need to convert this to seconds.

\[ 1 \text{ minute} = 60 \text{ seconds} \]

### Step 3: Convert the pressure from atm to Pascals
The pressure is given as 1.5 atm. We need to convert this to Pascals (Pa).

\[ 1 \text{ atm} = 1.013 \times 10^5 \text{ Pa} \]
\[ \text{Pressure} = 1.5 \text{ atm} = 1.5 \times 1.013 \times 10^5 \text{ Pa} = 1.5195 \times 10^5 \text{ Pa} \]

### Step 4: Calculate the work done
The work done by the machine can be calculated using the formula:

\[ \text{Work} = \text{Pressure} \times \text{Volume} \]

Since we are calculating the work done per minute, we can use:

\[ \text{Work} = \text{Pressure} \times \text{Volume} \]
\[ = (1.5 \times 1.013 \times 10^5) \times (60 \times 10^{-6}) \]
\[ = (1.5195 \times 10^5) \times (60 \times 10^{-6}) = 9.117 \text{ J} \]

### Step 5: Calculate the power delivered by the machine
Power is defined as work done per unit time. Therefore, we can calculate the power using the formula:

\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]
\[ = \frac{9.117 \text{ J}}{60 \text{ s}} = 0.15195 \text{ W} \approx 0.15 \text{ W} \]

### Final Answer
The power delivered by the machine is approximately **0.15 Watts**.

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