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Question: If two liquids of same masses but densities \(\rho _ { 2 }\) respectively are mixed, then density of...

If two liquids of same masses but densities ρ2\rho _ { 2 } respectively are mixed, then density of mixture is given by

A

ρ=ρ1+ρ22\rho = \frac { \rho _ { 1 } + \rho _ { 2 } } { 2 }

B

ρ=ρ1+ρ22ρ1ρ2\rho = \frac { \rho _ { 1 } + \rho _ { 2 } } { 2 \rho _ { 1 } \rho _ { 2 } }

C

ρ=2ρ1ρ2ρ1+ρ2\rho = \frac { 2 \rho _ { 1 } \rho _ { 2 } } { \rho _ { 1 } + \rho _ { 2 } }

D

ρ=ρ1ρ2ρ1+ρ2\rho = \frac { \rho _ { 1 } \rho _ { 2 } } { \rho _ { 1 } + \rho _ { 2 } }

Answer

ρ=2ρ1ρ2ρ1+ρ2\rho = \frac { 2 \rho _ { 1 } \rho _ { 2 } } { \rho _ { 1 } + \rho _ { 2 } }

Explanation

Solution

ρ= Total mass  Total volume =2mV1+V2=2mm(1ρ1+1ρ2)\rho = \frac { \text { Total mass } } { \text { Total volume } } = \frac { 2 m } { V _ { 1 } + V _ { 2 } } = \frac { 2 m } { m \left( \frac { 1 } { \rho _ { 1 } } + \frac { 1 } { \rho _ { 2 } } \right) }

∴ρ=2ρ1ρ2ρ1+ρ2\rho = \frac { 2 \rho _ { 1 } \rho _ { 2 } } { \rho _ { 1 } + \rho _ { 2 } }