find the density of a material of a cube floats on water with 1/3 of it in air (density of water 1000kg/m3
Answers
Answer:
Archimedes principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid.
So, for an object to float
Weight of object=F
B
(Buoyant force)
ρ
0
− density of an object
V
0
− volume of object
ρ
l
− density of liquid
V
dis
− Volume of disp. liquid
V
above
− Volume above the liquid
ρ
ω
− density of water
⇒ρ
0
V
0
g=ρ
l
v
dis
g
⇒ρ
l
=
V
dis
ρ
0
V
0
ρ
l
=
V
0
−V
above
ρ
0
V
0
→(i)
A/Q cube in water
V
above
=1/3V
)
From (i)
ρ
ω
=ρ
0
V
0
−
3
1
V
0
V
0
⇒ρ
ω
=
2
3
ρ
0
→(ii)
Cube in liquid
V
above
=3/5V
0
From (i)
⇒ρ
l
=ρ
0
V
0
−3/5V
0
V
0
⇒ρ
l
=
2
5
ρ
0
→(iii)
From (ii)&(iii)
ρ
l
=
2
5
×
3
2
ρ
ω
⇒ρ
l
=
3
5
ρ
ω
As
ρ
ω
=1 So,
ρ
l
=5/3
Explanation: