Two substances of densities {rho _1} and {rho | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) When substances are mixed in equal volumes,the density of the mixture is given by $\rho_{mix} = \frac{\rho_1 + \rho_2}{2}$.Given $\rho_{mix} = 4$,

Vedclass · Accepted Answer

${\rho _1} = 6$ and ${\rho _2} = 2$

Vedclass · Answer

(A) When substances are mixed in equal volumes,the density of the mixture is given by $\rho_{mix} = \frac{\rho_1 + \rho_2}{2}$.Given $\rho_{mix} = 4$,so $\frac{\rho_1 + \rho_2}{2} = 4$,which implies $\rho_1 + \rho_2 = 8$ .......$(i)$When substances are mixed in equal masses,the density of the mixture is given by $\rho_{mix} = \frac{2\rho_1 \rho_2}{\rho_1 + \rho_2}$.Given $\rho_{mix} = 3$,so $\frac{2\rho_1 \rho_2}{\rho_1 + \rho_2} = 3$,which implies $2\rho_1 \rho_2 = 3(\rho_1 + \rho_2)$ .......$(ii)$Substituting equation $(i)$ into equation $(ii)$:$2\rho_1 \rho_2 = 3(8) = 24$,so $\rho_1 \rho_2 = 12$.We have $\rho_1 + \rho_2 = 8$ and $\rho_1 \rho_2 = 12$. These are the roots of the quadratic equation $x^2 - 8x + 12 = 0$.$(x - 6)(x - 2) = 0$,so $x = 6$ or $x = 2$.Thus,the values are ${\rho _1} = 6$ and ${\rho _2} = 2$ (or vice versa).

Two substances of densities ${\rho _1}$ and ${\rho _2}$ are mixed in equal volumes and the relative density of the mixture is $4$. When they are mixed in equal masses,the relative density of the mixture is $3$. The values of ${\rho _1}$ and ${\rho _2}$ are

Similar Questions

Why is walking barefooted on a sharp gravel (grit) road difficult?

Three liquids of densities $d$,$2d$,and $3d$ are mixed in equal proportions of weights. The relative density of the mixture is

The density of the atmosphere at sea level is $1.29 \; kg/m^3$. Assume that it does not change with altitude. Then how high (in $km$) would the atmosphere extend?

$A$ beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out,the pressure in the liquid near the bottom of the liquid will

$A$ bubble from the bottom of a lake rises to its surface. Its volume doubles in the process. Assuming isothermal conditions, atmospheric pressure $= 75 \, cm$ of $Hg$, and the ratio of the densities of mercury and water $= 40/3$. The depth of the lake will be ..... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module