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 motor pump in kilowatts, we can follow these steps:

### Step 1: Understand the Problem
The motor pump lifts 6 tonnes of water from a height of 25 m to a height of 35 m. The time taken for this lift is 20 seconds. We need to calculate the power of the pump.

### Step 2: Calculate the Mass of Water
The mass of water lifted is given as 6 tonnes. We need to convert this into kilograms:
\[ \text{Mass} = 6 \text{ tonnes} = 6 \times 1000 \text{ kg} = 6000 \text{ kg} \]

### Step 3: Determine the Height Lifted
The height lifted by the pump is the difference in height:
\[ \text{Height} = 35 \text{ m} - 25 \text{ m} = 10 \text{ m} \]

### Step 4: Calculate the Work Done
The work done (W) by the pump in lifting the water can be calculated using 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 lifted)

Substituting the values:
\[ W = 6000 \text{ kg} \cdot 10 \text{ m/s}^2 \cdot 10 \text{ m} = 600000 \text{ J} \quad (\text{Joules}) \]

### Step 5: Calculate Power
Power (P) is defined as the work done per unit time. The formula for power is:
\[ P = \frac{W}{t} \]
Where \( t = 20 \text{ seconds} \).

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

### Step 6: Convert Power to Kilowatts
Since 1 kW = 1000 W, we convert the power from watts to kilowatts:
\[ P = \frac{30000 \text{ W}}{1000} = 30 \text{ kW} \]

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

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