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A test tube of uniform cross section is floated vertically in a liquid A with density pA upto a mark on it when it is filled with x ml of a liquid B of density pB. 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.
Asked by prarthana.c81 | 21 Nov, 2019, 08:09: PM
Let m be the mass of the test-tube and V be the volume upto the mark.
We know,
density, ρ = mV
Thus, mass of liquid A = ρA V
and mass of liquid B = ρB x

From the first case,
A = m + ρB x
→ V = (m + ρB x)/ρA ... (1)

And from second case, when test-tube must float in liquid B upto same mark when filled with 'y' mL of liquid A is given by,
B = m + ρA

→V = (m + ρAy)/ρB ... (2)

Equating (1) and (2), we get,
(m + ρB x)/ρA = (m + ρAy)/ρB

Solving this we get,

Answered by Shiwani Sawant | 22 Nov, 2019, 01:59: PM

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