Final answer:
The correct characteristic properties of upthrust are (i) the smaller the volume of a body submerged in a liquid, the smaller is the upthrust, and (ii) the upthrust acts on the body in an upward direction at the centre of buoyancy. Statement (iii) is incorrect, and thus the answer is option A (i) & (ii).
Step-by-step explanation:
To determine which characteristic properties of upthrust (buoyant force) are correct, let's examine each statement provided in the question:
- (i) the smaller the volume of a body submerged in a liquid, the smaller is the upthrust.
- (ii) the upthrust acts on the body in an upward direction at the centre of buoyancy.
- (iii) for the same volume of a body inside a fluid, the less the density of the fluid, greater will be the upthrust.
Now, let's address these statements one by one:
- Statement (i) is correct. Upthrust depends on the volume of fluid displaced by the submerged part of the body. According to Archimedes' principle, the buoyant force (upthrust) on an object is equal to the weight of the fluid displaced by the object. Therefore, if you have a smaller volume submerged, you displace less fluid and experience a smaller upthrust.
- Statement (ii) is also correct. The upthrust or buoyant force indeed acts upward through the centre of buoyancy, which is the centroid of the displaced volume of fluid.
- However, statement (iii) is incorrect. If the density of the fluid decreases but the volume inside remains the same, the weight of the fluid displaced (and hence the upthrust) will be less, not greater.
Therefore, the correct properties of upthrust are (i) and (ii), which means answer A is the correct choice.