Question

a piece of wood with uniform cross section and height 15 cm floats vertically with its height 10 cm in water and 12 cm in spirit. Find the density of wood nd spirit

Answer 1

Given:
let density of wood , water and spirit be ρ ,ρ₁and ρ₂ respectively.
Area of wooden piece=A
Volume of Wooden Piece=V=15A
volume Of water displaced(V1)=10A
Volume of spirit displaced(V2)=12A
To find density of Wood:
According to Archimedes principle:
weight of wood=weight of water displaced

Vρg=V1ρ₁g     [∵ W=mg]
ρ=(V1/V)*ρ₁
=(10A/15A)*1 [since density of water is 1gm/cm3]
=10/15
=0.67g/cm³
∴ Density of wood is 0.67g/cm³
To find density of Spirit:
weight of spirit=weight of wood
V2ρ₂g=Vρg
ρ₂=(V/V2)ρ
=(15A/12A)xρ
=(15/12)x0.67
=0.83g/cm³
∴ Density of spirit is 0.83g/cm³