a piece of wood of uniform cross section and height 15 CM floats vertically with its height 10 centimetre in water and 12 CM in Spirit find the density of wood and spirit
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Let density of Wood, Water and Spirit be ρ ,ρ₁ and 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
[ Thank you! for asking the question. ]
Hope it helps!
Let density of Wood, Water and Spirit be ρ ,ρ₁ and 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
[ Thank you! for asking the question. ]
Hope it helps!
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