Question

if two liquids of same masses but different densities p1 and p2 are mixed,then density of mixture is given by (a)p=p1+p2/2 (b)p=p1+p2/2p1p2 (c)2p1p2/p1+p2 (d)p1p2/p1+p2

Answer 1

"Given that, Two liquids consider liquid A and liquid B having same masses but are having different densities p1 and p2. When the two liquids are mixed, then the density of their mixture i

Density of liquid A = p1 and its mass = m

Density of liquid B = p2 and its mass = m

Because both the liquids are having equal mass

Therefore,

Volume of liquid A  $VA\quad =\quad \frac { m }{ p1}$

Volume of liquid B $VB\quad =\quad \frac { m }{ p2}$

Hence the total volume of the mixture= $V =\quad VA+VB\quad =\quad (\frac { m }{ p1} )+(\frac { m }{ p2} )$

Therefore its total mass is denoted as mA + mB;

Being both the masses of Liquid A and B are same then m+m = 2m

Density of mixture = mass of mixture /volume of mixture

$P\quad =\quad \frac { 2m }{ (\frac { m }{p1 } )} +(\frac { m }{p2} ) (By simplifying)$

$P\quad =\quad \frac { 2p1p2}{p1} +p2$

Hence, the density of mixture is$P\quad =\quad \frac { 2p1p2}{ p1 } +p2$"

Answer 2

Explanation:

Given that, Two liquids consider liquid A and liquid B having same masses but are having different densities p1 and p2. When the two liquids are mixed, then the density of their mixture i

Density of liquid A = p1 and its mass = m

Density of liquid B = p2 and its mass = m

Because both the liquids are having equal mass

Therefore,

Volume of liquid A VA\quad =\quad \frac { m }{ p1}VA=

p1

m

Volume of liquid B VB\quad =\quad \frac { m }{ p2}VB=

p2

m

Hence the total volume of the mixture= V =\quad VA+VB\quad =\quad (\frac { m }{ p1} )+(\frac { m }{ p2} )V=VA+VB=(

p1

m

)+(

p2

m

)

Therefore its total mass is denoted as mA + mB;

Being both the masses of Liquid A and B are same then m+m = 2m

Density of mixture = mass of mixture /volume of mixture

P\quad =\quad \frac { 2m }{ (\frac { m }{p1 } )} +(\frac { m }{p2} ) (By simplifying)P=

(

p1

m

)

2m

+(

p2

m

)(Bysimplifying)

P\quad =\quad \frac { 2p1p2}{p1} +p2P=

p1

2p1p2

+p2

Hence, the density of mixture isP\quad =\quad \frac { 2p1p2}{ p1 } +p2P=

p1

2p1p2

+p2 "