We study water of 1.0 g/cm3 density in an open container with its surface exposed to the atmosphere. If we measure the pressure first at a depth d and find the value p1, and then at twice that depth to find p2, the two results are related in this form:
a) p1> p2
b) p1=p2
c) 2 p1> p2
d) 2 p1 = p2
e) 2 p1< p2
Remember that atmospheric pressure is always added to a term that is proportional to depth. That should help you choose the correct answer.
so its d right
d) is NOT right. You ignored what I said about the atmospheric pressure term that gets added
To understand the relationship between the measured pressures at different depths in an open container of water, we need to consider the concept of hydrostatic pressure.
Hydrostatic pressure is the pressure exerted by a fluid due to its weight. It increases with depth since the weight of the fluid above creates an additional force. Mathematically, the hydrostatic pressure can be expressed as P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.
Given that we are studying water with a density of 1.0 g/cm³, we can simplify the equation to P = gh.
Now let's analyze the given scenario. We have two measurement points: first at depth d and then at twice that depth (2d).
At depth d, the pressure is P1 = gd.
At depth 2d, the pressure is P2 = g(2d).
Comparing the two expressions, we observe that P2 = 2P1.
Therefore, the correct answer is d) 2 p1 = p2.
The measured pressure at twice the depth (P2) is twice the pressure at the initial depth (P1).