The amount of work done in pumping water out of a cubical vessel of height 1 m is nearly `( g = 10 ms^(-2))`

Options

A. 10 J
B. 50 J
C. 500 J
D. 5000 J

Answer

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

### Step 1: Understand the dimensions of the vessel
The vessel is a cube with a height (H) of 1 meter. Since it is a cube, all sides are equal, which means the length of each side is also 1 meter.

### Step 2: Calculate the volume of water in the vessel
The volume (V) of a cube is given by the formula:
\[ V = \text{side}^3 = H^3 \]
Substituting the height:
\[ V = 1^3 = 1 \, \text{m}^3 \]

### Step 3: Calculate the mass of the water
The mass (m) of the water can be calculated using the formula:
\[ m = \text{Volume} \times \text{Density} \]
The density of water is approximately \( 1000 \, \text{kg/m}^3 \).
Thus,
\[ m = 1 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 1000 \, \text{kg} \]

### Step 4: Calculate the weight of the water
The weight (W) of the water can be calculated using the formula:
\[ W = m \times g \]
Where \( g \) is the acceleration due to gravity (given as \( 10 \, \text{m/s}^2 \)).
Thus,
\[ W = 1000 \, \text{kg} \times 10 \, \text{m/s}^2 = 10000 \, \text{N} \]

### Step 5: Determine the displacement of the water
When pumping the water out, the center of mass of the water is initially at a height of \( \frac{H}{2} \) from the bottom of the cube. Since \( H = 1 \, \text{m} \):
\[ \text{Displacement} = \frac{H}{2} = \frac{1}{2} = 0.5 \, \text{m} \]

### Step 6: Calculate the work done
The work done (W_d) in pumping the water out can be calculated using the formula:
\[ W_d = \text{Force} \times \text{Displacement} \]
Here, the force is equal to the weight of the water:
\[ W_d = W \times \text{Displacement} = 10000 \, \text{N} \times 0.5 \, \text{m} = 5000 \, \text{J} \]

### Final Answer
The amount of work done in pumping the water out of the cubical vessel is approximately:
\[ \boxed{5000 \, \text{J}} \]

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