A cubical vessel of height `1` m is full of water. What is the workdone in pumping water out of the vessel?

Options

A. 1250 J
B. 5000 J
C. 1000 J
D. 2500 J

Explanation

To find the work done in pumping water out of a cubical vessel of height 1 meter, we can follow these steps:

### Step 1: Determine the Volume of Water
The vessel is cubical with a height of 1 meter. Therefore, the volume \( V \) of the water in the vessel can be calculated as:
\[ V = \text{side}^3 = 1^3 = 1 \, \text{m}^3 \]

### Step 2: Calculate the Mass of Water
Using the density of water, which is approximately \( \rho = 1000 \, \text{kg/m}^3 \), we can find the mass \( m \) of the water:
\[ m = V \times \rho = 1 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 1000 \, \text{kg} \]

### Step 3: Determine the Height to Pump Water
Since we are pumping the water out of the vessel, we need to consider the average height from which the water is lifted. For a cubical vessel, the average height \( h \) of the water being pumped out is half the height of the vessel:
\[ h = \frac{1}{2} \, \text{m} = 0.5 \, \text{m} \]

### Step 4: Calculate the Work Done
The work done \( W \) in lifting the water can be calculated using the formula:
\[ W = mgh \]
Substituting the known values:
\[ W = 1000 \, \text{kg} \times 10 \, \text{m/s}^2 \times 0.5 \, \text{m} \]
\[ W = 1000 \times 10 \times 0.5 = 5000 \, \text{J} \]

### Final Answer
The work done in pumping the water out of the vessel is \( 5000 \, \text{J} \).

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