A tank is situated at a height of 60m from a pond. The capacity of the tank is `20m^(3)`. If this tank is completely filled by a pump from the water of pond in 3h 16 min then what is the power of pump?

Options

A. 2000W
B. 3000W
C. 4000W
D. 1000W

Explanation

To solve the problem, we need to calculate the power of the pump that fills a tank with water from a pond. Here’s a step-by-step breakdown of the solution:

### Step 1: Convert the time taken to fill the tank into seconds.
The time given is 3 hours and 16 minutes. We need to convert this into seconds.

- 1 hour = 60 minutes
- Therefore, 3 hours = 3 × 60 = 180 minutes
- Total time in minutes = 180 + 16 = 196 minutes
- Now, convert minutes to seconds:
\[ \text{Total time in seconds} = 196 \text{ minutes} \times 60 \text{ seconds/minute} = 11760 \text{ seconds} \]

### Step 2: Calculate the mass of the water in the tank.
The capacity of the tank is given as 20 m³. To find the mass of the water, we use the formula:
\[ \text{Mass} = \text{Volume} \times \text{Density} \]
Assuming the density of water is \(1000 \, \text{kg/m}^3\):
\[ \text{Mass} = 20 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 20000 \, \text{kg} \]

### Step 3: Calculate the work done to lift the water.
The work done (W) against gravity to lift the water to a height (h) is given by:
\[ W = mgh \]
Where:
- \(m = 20000 \, \text{kg}\) (mass of the water)
- \(g = 9.8 \, \text{m/s}^2\) (acceleration due to gravity)
- \(h = 60 \, \text{m}\) (height)

Substituting the values:
\[ W = 20000 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 60 \, \text{m} \]
\[ W = 20000 \times 9.8 \times 60 = 11760000 \, \text{J} \]

### Step 4: Calculate the power of the pump.
Power (P) is defined as work done per unit time:
\[ P = \frac{W}{t} \]
Where:
- \(W = 11760000 \, \text{J}\)
- \(t = 11760 \, \text{s}\)

Substituting the values:
\[ P = \frac{11760000 \, \text{J}}{11760 \, \text{s}} = 1000 \, \text{W} \]

### Final Answer:
The power of the pump is **1000 Watts**.

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