(a)
The specific gravity of the disk.
(a)
Answer to Problem 37P
The specific gravity of the disk is
Explanation of Solution
The specific gravity of a substance is the ratio of its density to the density of water.
Write the equation for specific gravity of the disk.
Here,
Write the equation for density.
Here,
Conclusion:
Substitute equation (II) in equation (I).
Substitute
Therefore, the specific gravity of the disk is
(b)
The distance of the water level at its bottom surface.
(b)
Answer to Problem 37P
The distance of the water level at its bottom surface is
Explanation of Solution
Write the equation for buoyant force is equal to the weight of the fluid displaced.
Here,
Since the relationship between the fraction of a floating object’s volume that is submerged and the ratio of the object’s density to that of the fluid in which it floats is rewritten from the equation (IV).
The ratio of the density of the disk to that of water is equal to the fraction of the volume of the disk is submerged.
Here,
Compare equation (VI) and (I).
Replace
Here,
Solve the equation (VII) for
Conclusion:
Substitute
Convert the above value into centimeter.
Therefore, the distance of the water level at its bottom surface is
(c)
The distance of the water level at its top surface.
(c)
Answer to Problem 37P
The distance of the water level at its top surface is
Explanation of Solution
From the equation (VII), find the distance of the top surface of the disk above the water level.
Replace
Here,
Rewrite equation (IX) by using equation (VIII).
Conclusion:
Substitute
Convert the above value into centimeter.
Therefore, the distance of the water level at its top surface is
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