Problem 2 (10 pts) Post - graduation, working a temporary menial job, your boss

Question

Problem 2 (10 pts) Post - graduation, working a temporary menial job, your boss assigns you a fluid statics problem in his exceedingly underfunded lab. You are to determine the density of an unknown fluid using a cylindrical test tube of diameter 2 cm. First, you drop the test tube vertically into water (Pw = 1000 kg/m^3), and mark the level (of the water - air interface) on the tube. Next, you drop the tube into the mystery fluid (p?), marking the level of the fluid - air interface. You observe that the mark for water is 0.5 cm above the mystery fluid - air interface. The height of the original water mark is 10 cm from the bottom of the tube. What is the density of the mystery fluid, p??

Explanation / Answer

here,

let's assume the weight of tube is W

when the test tube is dropped vertically in water the amount of water diaplace is equal to weight of test tube

w = pw * A * g * h

w = 10 * 1000 A*g

Now for the mysterious fluid

h'= (10 - 0.5) = 9.5cm

w = p? * A * g * 9.5

therefore,

10 * 1000 * A * g = p? * A * g * 9.5

p? = 1052.63 kgm^3

The density of unknown fluid is 1052.63 kgm^3

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