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Following are some statements about buoy...

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 immersed in the liquid) is placed inside the liquid. Of these statements :

A

Only (i),(ii) and (iii),(iv) are correct

B

Only (ii) is correct

C

Only (iii) and (iv) are correct

D

(i),(ii) and (iv) are incorrect

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the statements about buoyant force, we will evaluate each statement one by one based on the principles of fluid mechanics. ### Step-by-Step Solution: 1. **Statement (i): Buoyant force depends upon the orientation of the concerned body inside the liquid.** - **Analysis**: This statement is **false**. The buoyant force acting on a body submerged in a fluid depends only on the volume of fluid displaced by the body and the density of the fluid, not on the orientation of the body. Therefore, this statement is incorrect. 2. **Statement (ii): Buoyant force depends upon the density of the body immersed.** - **Analysis**: This statement is also **false**. The buoyant force does not depend on the density of the body itself but rather on the density of the fluid in which the body is immersed. The buoyant force is given by the formula \( F_b = \rho_{fluid} \cdot V_{displaced} \cdot g \), where \( \rho_{fluid} \) is the density of the fluid, \( V_{displaced} \) is the volume of fluid displaced, and \( g \) is the acceleration due to gravity. Thus, this statement is incorrect. 3. **Statement (iii): Buoyant force depends on the fact whether the system is on the moon or on the earth.** - **Analysis**: This statement is **true**. The buoyant force is influenced by the acceleration due to gravity. Since the acceleration due to gravity on the Moon is about 1/6th that of Earth, the buoyant force will indeed be different when comparing the two locations. Therefore, this statement is correct. 4. **Statement (iv): Buoyant force depends upon the depth at which the body (fully immersed in the liquid) is placed inside the liquid.** - **Analysis**: This statement is **false**. The buoyant force acting on a fully submerged body does not depend on the depth of immersion. It is determined solely by the volume of fluid displaced and the density of the fluid. The pressure at a particular depth does affect the force, but the buoyant force itself remains constant for a fully submerged object regardless of its depth. Thus, this statement is incorrect. ### Conclusion: - The only correct statement is **(iii)**. Therefore, the answer is that only statement (iii) is true. ### Final Answer: Only statement (iii) is true.
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