Upon which of the following quantities,the value of buoyant force on a body immersed in a fluid , does not depend -

Options

A. density of fluid
B. density of immersed body
C. volume of immersed body
D. acceleration due to gravity .

Answer

To determine the quantity upon which the value of buoyant force on a body immersed in a fluid does not depend, we will analyze the factors that influence buoyant force according to Archimedes' Principle.

### Step-by-Step Solution:

1. **Understanding Buoyant Force**:
- The buoyant force (Fb) acting on an object submerged in a fluid is defined by Archimedes' Principle. It states that the buoyant force is equal to the weight of the fluid displaced by the object.

2. **Formula for Buoyant Force**:
- The formula for buoyant force can be expressed as:
\[ F_b = \text{Weight of displaced liquid} = \text{Mass of displaced liquid} \times g \]
- Where \( g \) is the acceleration due to gravity.

3. **Mass of Displaced Liquid**:
- The mass of the displaced liquid can be calculated using the density of the liquid (\( \rho_{liquid} \)) and the volume of the displaced liquid (\( V_d \)):
\[ \text{Mass of displaced liquid} = \rho_{liquid} \times V_d \]

4. **Volume of Displaced Liquid**:
- The volume of the displaced liquid is equal to the volume of the object that is submerged in the fluid. If the object is fully immersed, then:
\[ V_d = V_{object} \]

5. **Complete Expression for Buoyant Force**:
- Substituting the expressions into the formula for buoyant force, we have:
\[ F_b = \rho_{liquid} \times V_{object} \times g \]
- From this expression, we can see that the buoyant force depends on:
- The density of the liquid (\( \rho_{liquid} \))
- The volume of the object (\( V_{object} \))
- The acceleration due to gravity (\( g \))

6. **Identifying the Independent Quantity**:
- The question asks for the quantity upon which the buoyant force does not depend. Among the factors:
- Density of the fluid: **Depends**
- Volume of the immersed body: **Depends**
- Acceleration due to gravity: **Depends**
- Density of the immersed body: **Does not depend** on buoyant force.

### Conclusion:
The buoyant force does not depend on the density of the immersed body. Therefore, the answer is that the buoyant force does not depend on the density of the immersed body.