Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2).
Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2).

According to the question, the diameter of the first bore is

d1 = 3.0 mm = 3 × 10-3 m
The radius of the first bore is

r= 3/2 = 1.5 x 10-3 m.
The diameter of the second bore is

d2 =6mm
The radius of the second bore is

r= 6/2 = 3 x 10-3 mm
The surface tension of water is

s = 7.3 × 10-2 N /m
The angle of contact between the bore surface and water is

θ= 0
And the density of water is

ρ =1.0 × 103 kg/m-3
Acceleration due to gravity, g = 9.8 m/s2
Let h1 and h2 be the corresponding heights to which water rises in the first and second tubes.
As a result, the height differences can be writte using the expression of height

Therefore, 2.482 mm is the difference in the water levels of the two arms.