A motor pump lifts 6 tonnes of water from a height of 25 m to a height 35m from the ground floor in 20 seconds. The power of the pump (in kW) is `[g = 10 ms^(-2)]`

Options

A. 3
B. 12
C. 1.5
D. 6

Answer

To find the power of the pump, we can follow these steps:

### Step 1: Understand the problem
We need to lift 6 tonnes of water from a height of 25 meters to a height of 35 meters. The difference in height (h) is 10 meters (35 m - 25 m). The time taken (t) for this lift is 20 seconds.

### Step 2: Convert the mass of water to kilograms
1 tonne is equal to 1000 kg. Therefore, 6 tonnes of water is:
\[ \text{Mass (m)} = 6 \, \text{tonnes} \times 1000 \, \text{kg/tonne} = 6000 \, \text{kg} \]

### Step 3: Calculate the work done (W)
The work done in lifting the water is given by the formula:
\[ W = m \cdot g \cdot h \]
Where:
- \( m = 6000 \, \text{kg} \) (mass of water)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 10 \, \text{m} \) (height difference)

Substituting the values:
\[ W = 6000 \, \text{kg} \times 10 \, \text{m/s}^2 \times 10 \, \text{m} \]
\[ W = 6000 \times 10 \times 10 = 600000 \, \text{J} \]

### Step 4: Calculate the power (P)
Power is defined as the work done per unit time:
\[ P = \frac{W}{t} \]
Where:
- \( W = 600000 \, \text{J} \) (work done)
- \( t = 20 \, \text{s} \) (time taken)

Substituting the values:
\[ P = \frac{600000 \, \text{J}}{20 \, \text{s}} \]
\[ P = 30000 \, \text{W} \]

### Step 5: Convert power to kilowatts
1 kilowatt (kW) is equal to 1000 watts (W). Therefore:
\[ P = \frac{30000 \, \text{W}}{1000} = 30 \, \text{kW} \]

### Final Answer
The power of the pump is **30 kW**.

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