1) Height of the column of light liquid in the right arm: 12.6 cm
2) Height of heavy liquid increases by 0.64 cm
Explanation:
1)
The density of a substance is given by
where
m is the mass of the substance
V is its volume
For a liquid in a tube, the volume can be written as
where
A is the cross-sectional area of the tube
L is the length of the column of liquid
Therefore the formula can be rewritten as
For the light liquid in the right arm of the tube, we have:
m = 92 g (mass)
(density)
(cross-sectional area)
Therefore we can re-arrange the equation to find L, the height of the column of light liquid:
2)
The gauge pressure of a column of liquid is given by:
where
is the density of the liquid
g is the acceleration due to gravity
h is the height of the column of liquid
When the light liquid is added on the right side, a certain volume of heavy liquid is displacement from the right arm to the right arm, and its volume now becomes , where
is the cross-sectional area of the left arm
is the change in height of the heavy liquid on the left arm
is the cross-sectional area of the right arm
is the initial height of the heavy liquid displaced from the right arm
Since the volume of the liquid must remain the same,
(1)
Moverover, at equilibrium we know that the pressure on the two arms of the U-tube must be the same, so:
(2)
where here we have:
(density of the heavy liquid)
(density of the light liquid)
L = 12.6 cm (height of the light liquid in the right arm)
And substituting (1) into (2) and re-arranging for h1, we find by how much the level of heavy liquid increases in the left arm:
Learn more about pressure in a liquid:
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