Question

The pressure exerted by a certain liquid at a given point is directly proportional to the depth of the point beneath the surface of the liquid. The pressure at 30m is 80 newtons. What is exerted at 50m ?

Answer 1

The pressure exerted by the liquid at a depth of 50 meters is approximately 133.33 newtons, calculated by setting up a proportion based on the fact that the pressure is directly proportional to the depth.

Step-by-step explanation:

The question involves calculating the pressure exerted by a liquid at a certain depth, which is a concept from Physics, specifically fluid mechanics. According to the information given, the pressure exerted by the liquid is directly proportional to the depth. Therefore, if the pressure at 30 meters is 80 newtons, we can set up a proportion to find the pressure at a depth of 50 meters. The proportion is:
80 N (at 30m) / 30m = x N (at 50m) / 50m
To solve for the unknown pressure (x), multiply both sides of the equation by 50m:

80 N * (50m/30m) = x N
This gives a result of approximately 133.33 newtons as the pressure at a depth of 50 meters, assuming that the density of the liquid and gravity remains constant.
This calculation is a straightforward example of how pressure in a fluid increases linearly with depth, as stated by Pascal's Principle and the fact that the pressure exerted by a column of fluid is proportional to the height of the column, the density of the fluid, and the acceleration due to gravity.