Question

A piece of wood of uniform cross section and 15cm height sinks 10cm in water and 12cm in spirit. Find R.D. of wood and 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

Answer 2

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