(b) 7.4cm
Given the following variables:
the radius of a glass capillary tube as r,
the coefficient of surface tension of the liquid in the glass as σ,
the density of the liquid as ρ,
the angle of contact between the liquid and the walls of the tube as θ and;
the capillary rise or height to which the liquid rises in the tube as h.
The variables are related by the following relation;
h = (2 x σ cos θ) / (r x ρ x g) -------------------------------(i)
Where;
g = acceleration due to gravity.
Therefore from the question;
diameter of tube = 0.4mm
=> radius, r = (0.4 / 2)mm = 0.2mm = 0.0002m
θ = contact angle = 0°
σ = surface tension coefficient = σs = 0.073N/m
ρ = density of liquid (water) = 1000kg/m³ [a constant]
Taking g = 9.81m/s², substitute these values into equation (i) to calculate the capillary rise, h, as follows;
h = (2 x 0.073 cos 0) / (0.0002 x 1000 x 9.81)
h = (2 x 0.073 x 1) / (1.962)
h = 0.074m
Convert the result to cm by multiplying by 100 as follows;
0.074m x 100 = 7.4cm
Therefore the capillary rise of water in the tube is 7.4cm
The capillary rise of water in the tube is; B; 7.4 cm
We are given;
Diameter of tube; d = 0.4mm = 0.0004 m
Radius; r = d/2 = 0.0004/2 = 0.0002 m
Contact angle; θ = 0°
Surface tension coefficient; σ_s = 0.073 N/m
Density of liquid (water); ρ = 1000kg/m³ (constant value)
The formula for the capillary rise of the water is;
H = (2σ_s * cos θ)/(ρgr)
Plugging in the relevant values gives;
H = (2 * 0.073 * cos 0)/(1000 * 9.8 * 0.0002)
H = 0.074 m
Converting to cm gives;
H = 7.4 cm
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