AP EAPCET 24-Aug-2021 Shift 2 Paper

Given that, initially body is submerged into the water by (

4

5

) th volume of body.
i.e. Volume inside the water, Vi=

4

5

V
where, V be total volume of body.
According to law of floatation, Weight of body = Buoyant force
Mg=Viρg
⇒Vσ=Viρ
⇒σ=

Vi

V

ρ=

4

5

ρ ...(i)
where, σ be the density of body.
When oil is poured into water, (

V

2

) volume of body is under water and oil.
Let ρo be density oil, then again by using condition of floatation,
Mg=Fwalt+Foil
Vσg=Vwρg+Voilρo‌g
Vσ=

V

2

ρ+

V

2

ρo
V×

4

5

ρ=

Vρ

2

+

Vρo

2

[From Eq. (i)]
ρ0=(

4

5

−

1

2

)ρ×2=

3

5

ρ
Hence, density of oil w.r.t. water is

3

5

.