A body experiences an upthrust `F_(1)` in river water and `F_(2)` in sea water when dipped up to the same level.
Which is more `F_(1)` or `F_(2)`?Give reason

Answer

To determine which upthrust force is greater, \( F_1 \) (in river water) or \( F_2 \) (in sea water), we can follow these steps:

### Step 1: Understand the Concept of Upthrust
Upthrust, or buoyant force, is the upward force exerted by a fluid on an object submerged in it. According to Archimedes' principle, the upthrust experienced by an object is equal to the weight of the fluid displaced by the object.

### Step 2: Compare the Densities of River Water and Sea Water
Sea water is denser than river water. The density of sea water is approximately 1.025 g/cm³, while the density of river water is about 1.0 g/cm³. This means that for the same volume of water displaced, sea water will exert a greater weight compared to river water.

### Step 3: Apply Archimedes' Principle
According to Archimedes' principle, the upthrust \( F \) can be calculated using the formula:
\[ F = \text{Volume of fluid displaced} \times \text{Density of fluid} \times g \]
Where \( g \) is the acceleration due to gravity.

### Step 4: Analyze the Upthrust Forces
- For river water, the upthrust \( F_1 \) can be expressed as:
\[ F_1 = V \times \rho_{\text{river}} \times g \]
- For sea water, the upthrust \( F_2 \) can be expressed as:
\[ F_2 = V \times \rho_{\text{sea}} \times g \]
Where \( V \) is the volume of water displaced, \( \rho_{\text{river}} \) is the density of river water, and \( \rho_{\text{sea}} \) is the density of sea water.

### Step 5: Conclusion
Since \( \rho_{\text{sea}} > \rho_{\text{river}} \), it follows that:
\[ F_2 > F_1 \]
Thus, the upthrust \( F_2 \) in sea water is greater than the upthrust \( F_1 \) in river water.

### Final Answer
Therefore, \( F_2 \) (upthrust in sea water) is greater than \( F_1 \) (upthrust in river water) because sea water is denser than river water.

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