A pump is required to lift `800 kg` of water per minute from a 10 m deep well and eject it with speed of `20 kg m//s` . The required power in watts of the pump will be

Options

A. `6000`
B. `4000`
C. `5000`
D. `8000`

Explanation

To find the required power of the pump in watts, we need to calculate the total work done by the pump in lifting the water and ejecting it. Here's how we can do it step by step:

### Step 1: Calculate the work done in lifting the water
The work done (W_lift) in lifting the water can be calculated using the formula:
\[ W_{\text{lift}} = mgh \]
Where:
- \( m = 800 \, \text{kg} \) (mass of the water)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 10 \, \text{m} \) (height of the well)

Substituting the values:
\[ W_{\text{lift}} = 800 \times 10 \times 10 = 80000 \, \text{J} \]

### Step 2: Calculate the work done in ejecting the water
The work done (W_eject) in ejecting the water can be calculated using the formula:
\[ W_{\text{eject}} = \frac{1}{2} mv^2 \]
Where:
- \( m = 800 \, \text{kg} \) (mass of the water)
- \( v = 20 \, \text{m/s} \) (speed of the water being ejected)

Substituting the values:
\[ W_{\text{eject}} = \frac{1}{2} \times 800 \times (20)^2 \]
\[ W_{\text{eject}} = \frac{1}{2} \times 800 \times 400 = 160000 \, \text{J} \]

### Step 3: Calculate the total work done
Now, we can find the total work done (W_total) by adding the work done in lifting and ejecting:
\[ W_{\text{total}} = W_{\text{lift}} + W_{\text{eject}} \]
\[ W_{\text{total}} = 80000 + 160000 = 240000 \, \text{J} \]

### Step 4: Calculate the power of the pump
Power (P) can be calculated using the formula:
\[ P = \frac{W}{t} \]
Where:
- \( W = 240000 \, \text{J} \) (total work done)
- \( t = 60 \, \text{s} \) (time in seconds, since the pump lifts water per minute)

Substituting the values:
\[ P = \frac{240000}{60} = 4000 \, \text{W} \]

### Final Answer
The required power of the pump is **4000 watts**.

---