A 1.0 HP motor pumps out water from a well of depth 20 m and fills a water tank of volume 2238 litres at a height of 10 m from the ground. The running time of the motor to fill the empty tank is `(g=10ms^(-2))`

Options

A. 5min
B. 10min
C. 15min
D. 20min

Answer

To solve the problem, we will follow these steps:

### Step 1: Convert the volume of water to mass
Given the volume of the water tank is 2238 liters, we can find the mass of the water using the density of water.

\[ \text{Density of water} = 1000 \, \text{kg/m}^3 \quad (\text{or } 1 \, \text{kg/L}) \]

\[ \text{Mass of water} = \text{Volume} \times \text{Density} = 2238 \, \text{L} \times 1 \, \text{kg/L} = 2238 \, \text{kg} \]

### Step 2: Calculate the total height the water is lifted
The water is lifted from a depth of 20 m and then raised to a height of 10 m from the ground. Therefore, the total height \( h \) the water is lifted is:

\[ h = 20 \, \text{m} + 10 \, \text{m} = 30 \, \text{m} \]

### Step 3: Calculate the work done to lift the water
The work done \( W \) against gravity to lift the water can be calculated using the formula:

\[ W = mgh \]

Where:
- \( m = 2238 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)
- \( h = 30 \, \text{m} \)

Substituting the values:

\[ W = 2238 \, \text{kg} \times 10 \, \text{m/s}^2 \times 30 \, \text{m} = 670800 \, \text{J} \]

### Step 4: Calculate the power of the motor
The power of the motor is given as 1 HP. We convert this to watts:

\[ 1 \, \text{HP} = 746 \, \text{W} \]

### Step 5: Calculate the time taken to fill the tank
Power is defined as the work done per unit time:

\[ P = \frac{W}{t} \]

Rearranging for time \( t \):

\[ t = \frac{W}{P} \]

Substituting the values we have:

\[ t = \frac{670800 \, \text{J}}{746 \, \text{W}} \approx 897.6 \, \text{s} \]

### Step 6: Convert time from seconds to minutes
To convert seconds to minutes, we divide by 60:

\[ t \approx \frac{897.6 \, \text{s}}{60} \approx 14.96 \, \text{minutes} \approx 15 \, \text{minutes} \]

### Final Answer
The time taken to fill the empty tank is approximately **15 minutes**.

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