Final answer:
The force exerted by a fluid with a constant density at a depth is given by the formula Force = Pressure × Area.
This arises from the understanding that pressure is the weight of the fluid divided by the area over which it's distributed, and can be expressed as Force = (density × gravity × height) × Area.
So, the correct option is: A) Pressure × Area
Step-by-step explanation:
When considering the force exerted by the fluid vertically with its bottom 100 meters below the surface, it is important to understand the relationship between pressure, force, and area. Specifically, we are looking at the concept that pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
The formula for pressure due to the weight of a fluid of constant density is given by p = pgh, where p is the pressure, h is the depth of the fluid, p is the density of the fluid, and g is the acceleration due to gravity.
Given that the weight of the fluid is equal to its mass times the acceleration due to gravity (mg) and the weight can also be written as the product of the density, the volume of the fluid (V), and the acceleration due to gravity (pVg), the correct formula to find the force at the bottom of the container is Force = Pressure × Area.
This is seen through the fact that pressure is calculated as the weight of the fluid, mg, divided by the area A, which leads to the relationship Force = mg = pAhg = (pgh)A, where A is the area of the bottom of the container.