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 | 21st Nov, 2019, 08:09: PM

Expert Answer:

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 | 22nd Nov, 2019, 01:59: PM