Correct Answer - Option 4 :
\({2d_1d_2 \over d_1+d_2}\)
CONCEPT:
- The relation between mass, density, and volume is given by:
mass = density × Volume
m = d × V
EXPLANATION:
Given that both the fluids have the same mass. Let it is m.
The density of first fluid = d1
Volume of first fluid = V1 = m / d1 ................(i)
The density of second fluid = d2
Volume of second fluid = V2 = m / d2 ................(ii)
Now after mixing the fluids.
\(Density ~of~ mixture = {Total~mass \over Total ~volume}\)
\(Density ~of~ mixture = {m+m \over V_1+ V_2}\)
From eq (i) and (ii)
\(Density ~of~ mixture = {2m \over {m \over d_1}+ {m \over d_2}}\)
\(Density ~of~ mixture = {2 \over {1 \over d_1} + {1 \over d_2}}\)
\(Density ~of~ mixture = {2 d_1 d_2 \over {d_1 + d_2}}\)
So the correct answer is option 4.