A tube of uniform cross- section is made heavy at its bottom so that it can stand vertically in a liquid. prove that lenth of the tube in the liquid is inversely proportional to its density
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Let the height of the glycerin in the first arm be h
h
= 10cm=0.1m
Let the height of the water in the second arm be h
w
Density of the water = ρ
w
Density of glycerin = ρ
h
Let the level difference between the two free surfaces in the two limbs be x
Pressure at both levels is equal, therefore,
p
w
=p
h
ρ
h
gh
h
=ρ
w
gh
w
h
w
=h
h
+x
ρ
h
h
h
=ρ
w
h
h
+ρ
w
x
x=
ρ
w
ρ
h
h
h
−ρ
w
h
h
=
1000
m
3
kg
0.1(1200
m
3
kg
−1000
m
3
kg
)
=0.002m
Therefore the level difference = 2cm
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