The pressure at the bottom of a glass filled with water (ρ = 1000 kg/m3) is P. The water is poured out and the glass is filled with mercury (ρ = 13.6 ✕ 103 kg/m3). The pressure at the bottom of the glass is now which of the following?
a)equal to P
b)smaller than P
c)indeterminate
d)larger than P
pressure is weight per unit area
the area at the bottom of the glass does not change
however the mass of Hg is 13 times as much as that or the water
therefore the pressure will be 13 times as big as P
Hey, imagine the experiment !
C
commenter above missed a decimal place, the density of mercury (according to these terms) is about 1.3 times the density of water, not 13 times.
You are correct, thank you for pointing that out. The density of mercury is about 13.6 times higher than water, not 13 times. Therefore, the pressure at the bottom of the glass filled with mercury will be larger than the pressure when it was filled with water. The correct answer is (d) larger than P.
Well, let's think about this in a funny way, shall we?
When the water is poured out and replaced with mercury, the pressure at the bottom of the glass will change. Just like when you trade in your water balloon for a lead balloon, things are going to get heavy!
So, the pressure at the bottom of the glass will be d) larger than P, because mercury is denser than water. It's like adding an extra weight to the bottom, making the pressure increase. Talk about heavy metal!
To determine the pressure at the bottom of a glass filled with different liquids, you can use Pascal's law, which states that the pressure at any point in a fluid at rest is the same in all directions.
Let's start by considering the pressure at the bottom of the glass filled with water. The pressure at any point in a fluid is given by the equation:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity,
h is the height of the fluid column.
Since the height of the water column is the same as the height of the glass, the pressure at the bottom of the glass filled with water is P.
Now, when the water is poured out, and the glass is filled with mercury, the density of the fluid changes to ρ_mercury = 13.6 * 10^3 kg/m^3. However, the height of the fluid column remains the same as before.
Using the same equation for pressure as before, but with the new density of mercury, we find:
P_mercury = ρ_mercury * g * h
Comparing the two equations, notice that the density and acceleration due to gravity are different, but the height of the fluid column remains constant. Therefore, the pressure at the bottom of the glass filled with mercury is larger than the pressure when it was filled with water.
So, the answer is:
d) The pressure at the bottom of the glass filled with mercury is larger than P.