Question

When equal volumes of two substances are mixed, the specific gravity of mixture is 4. when equal mass of the above substances are mixed, the specific gravity of the mixture is 3. the specific gravity of the two substances would be?

Answer 1

Answer:

when substance a have specific gravity =6 then second have 2

when substance a have specific gravity =2 then second have 6

Step-by-step explanation:

Let ρ₁ and ρ₂ be the specific gravity of two liquids

When equal volume is mixed then

specific gravity= ρ

which is given by formula

ρ= (ρ₁+ρ₂)/2

As it is given that specific gravity = 4

so

4= (ρ₁+ρ₂)/2

ρ₁+ρ₂ = 8   ......................(i)

Now when equal masses are added

it is given by the formula

ρ= (2ρ₁ρ₂)/(ρ₁+ρ₂)

as ρ=3 so

3 (ρ₁+ρ₂)=(2ρ₁ρ₂)

3(8) =(2ρ₁ρ₂)

ρ₁ρ₂=$\frac{24}{2}$

ρ₁ρ₂=12                                   ....................(ii)

from equation (ii)

ρ₁=12/ρ₂

put it in (i)

12/ρ₂+ρ₂=8

ρ₂²+12=8ρ₂

ρ₂²+12-8ρ₂=0

ρ₂²-8ρ₂+12=0

using mid term breaking

ρ₂²-6ρ₂-2ρ₂+12=0

ρ₂(ρ₂-6)-2(ρ₂-6)=0

(ρ₂-6)(ρ₂-2)=0

so

ρ₂=6 or ρ₂=2

Now putting it in (i)

ρ₁=8-ρ₂

ρ₁=8-6 and ρ₁=8-2

ρ₁=2 or ρ₁=6