A test tube of uniform cross-section is floated vertically in a liquid 'A' (density `rho A`) upto a mark on it when it is filled with 'x' ml of a liquid 'B' (density `rho B`). To make the test tube float in liquid B upto the same mark it is filled with y ml of the liquid A. Find the mass of the test tube.

Explanation

(i) What is law of floatation ?
Is mass of the test tube (float)changed, when it is immersed in different liquids ?
Then, can we say that it is a constant immersion hydrometer ?
Assume the mass of the testtube =M.
When immersed in liquid 'A', the float is filled with 'x' ml of liquid B.
Then, find the weight of the float.
Is the volume of liquid 'B' in the float =x ml.
Then, weight of the liquid =vdg.
Now, the weight of the float `=mg +x rho B g`
Similarly, find the weight of the float when immersed in liquid 'B'.
Is the weight of the float `= mg+y rho A g`
But, weight of the float = weight of the displaced liquid.
The volume of the displaced liquids (both A and B) are equal.
Then get the volume of displaced liquids from above two cases in form of equations and equate them.
From this, obtain the mass of the test tube.
(ii) 51680 Pa