The buoyant force depends upon

Options

A. density of the liquid
B. volume of the body inside the liquid
C. value of g at that place
D. all the above

Answer

To determine what the buoyant force depends upon, we can analyze the factors involved in the buoyancy of an object submerged in a fluid. The buoyant force is the upward force exerted by a fluid on a submerged object, and it is described by Archimedes' Principle. Let's break down the steps to understand the dependencies of the buoyant force.

### Step-by-Step Solution:

1. **Understanding Buoyant Force**:
The buoyant force (F_b) is the upward force exerted by a fluid on an object that is submerged in it. According to Archimedes' Principle, this force is equal to the weight of the fluid that is displaced by the object.

2. **Weight of Displaced Fluid**:
The weight of the fluid displaced can be calculated using the formula:
\[ F_b = \text{Weight of fluid displaced} = \text{mass of fluid displaced} \times g \]
where \( g \) is the acceleration due to gravity.

3. **Mass of Displaced Fluid**:
The mass of the fluid displaced can be expressed as:
\[ \text{mass} = \text{density of fluid} \times \text{volume of fluid displaced} \]
Thus, we can rewrite the buoyant force as:
\[ F_b = \text{density of fluid} \times \text{volume of fluid displaced} \times g \]

4. **Identifying Dependencies**:
From the equation above, we can identify the three key factors that the buoyant force depends on:
- **Density of the fluid (\( \rho \))**: The greater the density of the fluid, the greater the buoyant force.
- **Volume of the object submerged in the fluid (\( V' \))**: The more volume of the object that is submerged, the greater the volume of fluid displaced, and hence, the greater the buoyant force.
- **Acceleration due to gravity (\( g \))**: The buoyant force also depends on the local value of \( g \). For example, \( g \) is different on the Moon compared to Earth.

5. **Conclusion**:
Therefore, the buoyant force depends on:
- The density of the liquid
- The volume of the body submerged in the liquid
- The value of \( g \) at the location of the liquid

Hence, the correct answer is that the buoyant force depends on all of the above factors.

### Final Answer:
The buoyant force depends on:
1. Density of the liquid
2. Volume of the body inside the liquid
3. Value of \( g \) at the place
4. **All of the above**