Question

1) one gram of substance of relative density 2 and 4 gram of another substance of relative density 3 are mix together. the relative density of the mixture is about?

1) two identical containers have liquid of different densities d1 and d2 but they weigh the same when kept on a weighing Pan .the density of the mixture when they are mixed together will be?

Answer 1

Relative density is the ratio of density of a substance to the density of water.
So, Density of the substance =Relative density x density of water

Hence for the substance m=1g, relative density= 2
Density = 2 x 1= 2g/cc [density of water is 1g/cc]
Density = Mass/Volume
2g/cc = 1g/v
v = 1/2cc

for the substance m=4g, relative density = 3
density = Relative density x density of water = 3 x 1 = 3g/cc
density = mass/v1
3 = 4/v1
v1 = 4/3cc

when they are mixed together total mass = 1+4 = 5g, and total volume = 1/2 + 4/3 = 11/6cc
density = m/v = 5/(11/6) = 30/11 = 2.72g/cc

Hence Relative density of the mixture = density of the mixture/density of water = 2.72/1 = 2.72 Ans.

2)
For liq 1, Density = d1 and Mass = m
For liq 2, Density = d2 and Mass = m

Vol of liq 1 = m/d1
Vol of liq 2 = m/d2

Total volume = m/d1 + m/d2 = m(d1+d2) / d1d2
Total mass = m+m= 2m

Density of the mixture = Total Mass/ Total Volume
=2m d1d2 / m(d1+d2)
= d1d2/(d1+d2)