If two liquids of same mass but densities `rho_1` and `rho_2` respectively are mixed, then the density of the mixture is:

Options

A. `rho=(rho_1+rho_2)/(2)`
B. `rho=(rho_1+rho_2)/(2rho_1rho_2)`
C. `rho=(2rho_1rho_2)/(rho_1+rho_2)`
D. `rho=(rho_1rho_2)/(rho_1+rho_2)`

Answer

C

Explanation

As `V_1=(M)/(rho_1)V_2=(M)(rho_2)`, volume of mixture ,`V=V_1+V_2=(M)/(rho_1)+(M)/(rho_2)=M((rho_2+rho_2)/(rho_1rho_2))`
mass of mixture, `M+M=2M`. Hence, density of the mixture, `rho=(2M)/(M((rho_1+rho_2))/(rho_1rho_2))=(2rho_1rho_2)/((rho_1+rho_2))`