Question

Which of the following is true for pressure exerted by a liquid?
(A) Pressure does not depend on depth
(B) Pressure is only exerted in the downward direction
(C) Pressure is directed both downwards and sideways, but downward pressure is greater than sideways pressure
(D) At the same depth pressure is same in all directions

Answer 1

Hint : Pressure in a liquid is a result of the weight of the substance above it (the substance above it could be other fluids like air or could be the liquid itself. If a substance does not move, then there must be equilibrium in all directions.

Complete step by step answer
Imagine a liquid in a container, open to the atmosphere and having a particular height. The pressure at the surface (on top) of the liquid is the atmospheric pressure. Now, imagine a ball of the liquid molecules moving downward into the liquid. As this is done, some of the liquid will be above the point. Hence, the weight of the liquid directly above the molecules will act on the molecules. Hence, the pressure on the molecules will be the weight of the liquid above divided by the area of the molecules. If the molecules are moved even more downward, the weight above it increases, hence, the pressure on the molecule increases. So the pressure depends on the depth. Now, this molecule could be chosen to be a part of the liquid itself, hence, like the rest of the liquid is in total equilibrium in all directions. This means that the pressure exerted on all sides must be equal to each other.
Hence, the correct option is D.

Note
For clarity, we say the pressure is equal in all direction because if the pressure exerted by the liquid on that ball of molecules for an example was greater in some direction (i.e. greater force in that direction), then the molecules will move in that direction (because they would be a net force in that direction). And since the hypothetical molecules could really be the molecules of the liquid, then the liquid molecules should be moving about and not static. But this is not so as we observe in the real world. Hence, the pressure must be equal in all directions.