A water container has water upto a height of 20 cm, volume 2 litres. Top of container has area 60 cm`""^(2)` and bottom has area of 20 cm`""^(2)`. The downward force exerted by water at the bottom will be.

Options

A. 200 N
B. 100 N
C. 222 N
D. 122 N

Explanation

To find the downward force exerted by water at the bottom of the container, we can follow these steps:

### Step 1: Convert the height of water to meters
The height of water in the container is given as 20 cm. We need to convert this to meters for our calculations.

\[ h = 20 \, \text{cm} = 0.20 \, \text{m} \]

### Step 2: Calculate the pressure at the bottom of the container
The pressure at a certain depth in a fluid is given by the formula:

\[ P = P_0 + \rho g h \]

Where:
- \( P_0 \) is the atmospheric pressure (approximately \( 1.01 \times 10^5 \, \text{Pa} \)),
- \( \rho \) is the density of water (\( 1000 \, \text{kg/m}^3 \)),
- \( g \) is the acceleration due to gravity (\( 10 \, \text{m/s}^2 \)),
- \( h \) is the height of the water column (in meters).

Substituting the values:

\[ P = 1.01 \times 10^5 \, \text{Pa} + (1000 \, \text{kg/m}^3)(10 \, \text{m/s}^2)(0.20 \, \text{m}) \]

Calculating the second term:

\[ P = 1.01 \times 10^5 \, \text{Pa} + 2000 \, \text{Pa} \]

\[ P = 1.01 \times 10^5 \, \text{Pa} + 2 \times 10^3 \, \text{Pa} = 1.03 \times 10^5 \, \text{Pa} \]

### Step 3: Calculate the area of the bottom of the container
The area of the bottom of the container is given as 20 cm². We need to convert this to square meters:

\[ A = 20 \, \text{cm}^2 = 20 \times 10^{-4} \, \text{m}^2 = 0.002 \, \text{m}^2 \]

### Step 4: Calculate the force exerted at the bottom of the container
The force exerted by the water at the bottom can be calculated using the formula:

\[ F = P \times A \]

Substituting the values we have:

\[ F = (1.03 \times 10^5 \, \text{Pa}) \times (0.002 \, \text{m}^2) \]

Calculating the force:

\[ F = 1.03 \times 10^5 \times 0.002 = 206 \, \text{N} \]

### Final Answer
The downward force exerted by the water at the bottom of the container is **206 N**.

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