1.

mercury is poured into a U-Tube in which the cross sectional area of the left hand limb is three times smaller than the right one the level of the mercury in the narrow limb is distance l = 30 cm from the upper end of the tube how much will the mercury level rise in the right limb if the left one is filled to the top with water

Answer»

Angle of contact between mercury and soda lime glass, θ = 140°
Radius of the narrow tube, r = 1 mm = 1 × 10–3 m
Surface tension of mercury at the given temperature, s = 0.465 N m–1
Density of mercury, ρ =13.6 × 103 kg/m3
DIP in the HEIGHT of mercury = H
Acceleration DUE to gravity, G = 9.8 m/s2
Surface tension is related with the angle of contact and the dip in the height as:
s = hρgr / 2 Cosθ
∴ h = 2s Cosθ / ρgr
= 2 × 0.465 × Cos1400 / (1 × 10-3 × 13.6 × 103 × 9.8)
= -0.00534 m
= -5.34 m
Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by 5.34 mm.


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