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Question

An empty glass test tube floats vertically in water to a depth of 5 cm. Now, on introducing a 8 cm liquid column into the tube, its depth in water is further Now the empty test tube is increased by 4 cm. N allowed to float vertically in the liquid, 5 cm of the tube is seen in air. Find the total length of the tube.

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Solution

Let cross sectional area of tube=A
length of tube=L
for equilibrium,
weight of tubeWT= buoyancy force by water
So,
WT= ρwgA×5
after pouring liquid,
WT=ρwgA×8=ρwgA×9
ρwgA5=ρwgA8=ρwgA9
ρl=ρw2.



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