Two vertical capillary limbs are connected at the bottom to form a U-shaped arrangement and contain the same perfectly wetting liquid. Their radii are 0.50 mm and 1.50 mm. For the liquid, S = 0.075 N/m, ρ = 1000 kg/m³ and g = 10 m/s². If the difference between the two capillary levels is N cm, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
JEE Mains NEET JEE Advanced

Question

Two vertical capillary limbs are connected at the bottom to form a U-shaped arrangement and contain the same perfectly wetting liquid. Their radii are 0.50 mm and 1.50 mm. For the liquid, S = 0.075 N/m, ρ = 1000 kg/m³ and g = 10 m/s². If the difference between the two capillary levels is N cm, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

For a perfectly wetting liquid, h = 2S/[ρgr]. For the smaller radius, r₁ = 0.50 mm, so h₁ = 3 cm. For the larger radius, r₂ = 1.50 mm, which is three times r₁. Therefore, h₂ = h₁/3 = 1 cm. Hence the level difference is Δh = h₁−h₂ = 3−1 = 2 cm. Therefore, N = 2.