Density and Following Condition Arises

Some important questions from Hydrostatics:
i. Why is it easier to lift a body in a liquid than in the air?
~ We know that,
Upthrust =Density of fluid*acceleration due to gravity*Immersed volume of the body
From the realtion above, it is clear that upthrust given by a fluid to a body is directly proportional to the density of the fluid. Also, as a matter of fact, the density of air is less than that of liquid. So, the liquid provides greater amount of upthrust than the air does. This implies that a body loses its weight greater in air than in the liquid. Therefore, it is easier to lift a body in a liquid than in the air.

ii. Steel balls sink in water but don’t sink in mercury. Why?
~ The density of the water is less than that of mercury. Also, the density of the steel is greater than that of water but less than that of mercury. Hence, mercury provides greater upthrust than water does resulting the floatation of the steel in it.

iii. A body floats in a liquid contained in a beaker. The whole system falls under gravity. What is the upthrust on the body due to liquid?
~ When a container filled with a liquid falls freely under the influence of gravity, the following condition arises.
Upthrust=mg-ma
Since the process is influenced by gravity, ma = mg
So, upthrust=0N
Hence, it is conclusively proved that the upthrust on the body is zero.

iv. Why do bigger air bubbles rise faster than the smaller ones in boiling water?
We know that,
Upthrust =Density of fluid*acceleration due to gravity*Immersed volume of the body
Bigger air bubbles means greater volume and vice versa. From the above relation, Upthrust provided by a liquid is directly proportion to the volume of the body. Hence, the bigger bubbles experience greater upthrust than that of the smaller ones. As a result, they rise faster to the surface of the water.