Following are some statements about buoyant force: (Liquid is of uniform density)
(i) Buoyant force depends upon orientation of the concerned body inside the liquid. (ii) Buoyant force depends upon the density of the body immersed. (iii) Buoyant force depends on the fact whether the system is on moon or on the earth. (iv) Buoyant force depends upon the depth at which the body (fully immeresed in the liquid) is placed inside the fluid. Of these statements:

Options

A. Only (i),(ii) and (iv) are correct.
B. Only (ii) is correct
C. Only (ii) and (iv) are correct
D. (i),(ii) and (iv) are incorrect

Explanation

To analyze the statements regarding buoyant force, we can break down the problem step by step.

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

### Step 2: Analyzing Each Statement
We will evaluate each statement one by one to determine its validity.

#### Statement (i): Buoyant force depends upon orientation of the concerned body inside the liquid.
- **Analysis**: The buoyant force is determined by the volume of fluid displaced, which is constant for a fully submerged object regardless of its orientation. Therefore, this statement is **incorrect**.

#### Statement (ii): Buoyant force depends upon the density of the body immersed.
- **Analysis**: The buoyant force depends on the density of the fluid, not the density of the object. The formula for buoyant force is \( F_b = \rho_{fluid} \cdot g \cdot V_{displaced} \), where \( \rho_{fluid} \) is the fluid's density. Thus, this statement is **incorrect**.

#### Statement (iii): Buoyant force depends on the fact whether the system is on moon or on the earth.
- **Analysis**: The buoyant force is influenced by the acceleration due to gravity (\( g \)). Since \( g \) is different on the Moon compared to Earth, the buoyant force will vary depending on the location. Therefore, this statement is **correct**.

#### Statement (iv): Buoyant force depends upon the depth at which the body (fully immersed in the liquid) is placed inside the fluid.
- **Analysis**: If an object is fully submerged, it displaces a volume of fluid equal to its own volume, and this does not change with depth. Thus, the buoyant force does not depend on the depth of immersion. Therefore, this statement is **incorrect**.

### Step 3: Conclusion
Based on the analysis:
- Statement (i) is incorrect.
- Statement (ii) is incorrect.
- Statement (iii) is correct.
- Statement (iv) is incorrect.

Thus, the correct option is that statements 1, 2, and 4 are incorrect, while statement 3 is correct.

### Summary of Correct Statements
- **Correct Statement**: Only statement (iii) is correct.