For a floating body, its weight W and upthrust `F_(B)` on it are related as

Options

A. `WgtF_(B)`
B. `WltF_(B)`
C. `W=F_(B)`
D. nothing can be said

Answer

To find the relationship between the weight \( W \) of a floating body and the upthrust \( F_B \) acting on it, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Upthrust**:
- When a body is placed in a fluid (like water), it experiences an upward force called upthrust (or buoyant force). This force is due to the pressure difference between the top and bottom of the submerged part of the body.

2. **Archimedes' Principle**:
- According to Archimedes' Principle, the upthrust (buoyant force) acting on a body immersed in a fluid is equal to the weight of the fluid displaced by the body.

3. **Weight of the Floating Body**:
- The weight \( W \) of the floating body is the force due to gravity acting on it.

4. **Equilibrium Condition for Floating Bodies**:
- For a body to float, the forces acting on it must be balanced. This means that the weight of the body must be equal to the upthrust acting on it. Therefore, we can write:
\[ W = F_B \]
- Here, \( W \) is the weight of the body and \( F_B \) is the upthrust (buoyant force).

5. **Conclusion**:
- Thus, we conclude that for a floating body, the relationship between its weight \( W \) and the upthrust \( F_B \) is given by:
\[ W = F_B \]